Loan Analysis (Prosper Provided) by Andrew Teixeira
Load all relevant libraries
Establish working directory
#Establishing the working directory
getwd()## [1] "/Users/andrewteixeira/Documents/DAND/Final_Project_EDA"Load the data into the variable “loans”
Examining the column names of the dataset ‘loans’ to get a sense of what is within the dataset.
#Examing the column names of the dataset 'loans' to get a sense of what is within the dataset.
names(loans)## [1] "ListingKey"
## [2] "ListingNumber"
## [3] "ListingCreationDate"
## [4] "CreditGrade"
## [5] "Term"
## [6] "LoanStatus"
## [7] "ClosedDate"
## [8] "BorrowerAPR"
## [9] "BorrowerRate"
## [10] "LenderYield"
## [11] "EstimatedEffectiveYield"
## [12] "EstimatedLoss"
## [13] "EstimatedReturn"
## [14] "ProsperRating..numeric."
## [15] "ProsperRating..Alpha."
## [16] "ProsperScore"
## [17] "ListingCategory..numeric."
## [18] "BorrowerState"
## [19] "Occupation"
## [20] "EmploymentStatus"
## [21] "EmploymentStatusDuration"
## [22] "IsBorrowerHomeowner"
## [23] "CurrentlyInGroup"
## [24] "GroupKey"
## [25] "DateCreditPulled"
## [26] "CreditScoreRangeLower"
## [27] "CreditScoreRangeUpper"
## [28] "FirstRecordedCreditLine"
## [29] "CurrentCreditLines"
## [30] "OpenCreditLines"
## [31] "TotalCreditLinespast7years"
## [32] "OpenRevolvingAccounts"
## [33] "OpenRevolvingMonthlyPayment"
## [34] "InquiriesLast6Months"
## [35] "TotalInquiries"
## [36] "CurrentDelinquencies"
## [37] "AmountDelinquent"
## [38] "DelinquenciesLast7Years"
## [39] "PublicRecordsLast10Years"
## [40] "PublicRecordsLast12Months"
## [41] "RevolvingCreditBalance"
## [42] "BankcardUtilization"
## [43] "AvailableBankcardCredit"
## [44] "TotalTrades"
## [45] "TradesNeverDelinquent..percentage."
## [46] "TradesOpenedLast6Months"
## [47] "DebtToIncomeRatio"
## [48] "IncomeRange"
## [49] "IncomeVerifiable"
## [50] "StatedMonthlyIncome"
## [51] "LoanKey"
## [52] "TotalProsperLoans"
## [53] "TotalProsperPaymentsBilled"
## [54] "OnTimeProsperPayments"
## [55] "ProsperPaymentsLessThanOneMonthLate"
## [56] "ProsperPaymentsOneMonthPlusLate"
## [57] "ProsperPrincipalBorrowed"
## [58] "ProsperPrincipalOutstanding"
## [59] "ScorexChangeAtTimeOfListing"
## [60] "LoanCurrentDaysDelinquent"
## [61] "LoanFirstDefaultedCycleNumber"
## [62] "LoanMonthsSinceOrigination"
## [63] "LoanNumber"
## [64] "LoanOriginalAmount"
## [65] "LoanOriginationDate"
## [66] "LoanOriginationQuarter"
## [67] "MemberKey"
## [68] "MonthlyLoanPayment"
## [69] "LP_CustomerPayments"
## [70] "LP_CustomerPrincipalPayments"
## [71] "LP_InterestandFees"
## [72] "LP_ServiceFees"
## [73] "LP_CollectionFees"
## [74] "LP_GrossPrincipalLoss"
## [75] "LP_NetPrincipalLoss"
## [76] "LP_NonPrincipalRecoverypayments"
## [77] "PercentFunded"
## [78] "Recommendations"
## [79] "InvestmentFromFriendsCount"
## [80] "InvestmentFromFriendsAmount"
## [81] "Investors"head(loans)## ListingKey ListingNumber ListingCreationDate
## 1 1021339766868145413AB3B 193129 2007-08-26 19:09:29.263000000
## 2 10273602499503308B223C1 1209647 2014-02-27 08:28:07.900000000
## 3 0EE9337825851032864889A 81716 2007-01-05 15:00:47.090000000
## 4 0EF5356002482715299901A 658116 2012-10-22 11:02:35.010000000
## 5 0F023589499656230C5E3E2 909464 2013-09-14 18:38:39.097000000
## 6 0F05359734824199381F61D 1074836 2013-12-14 08:26:37.093000000
## CreditGrade Term LoanStatus ClosedDate BorrowerAPR BorrowerRate
## 1 C 36 Completed 2009-08-14 00:00:00 0.16516 0.1580
## 2 36 Current 0.12016 0.0920
## 3 HR 36 Completed 2009-12-17 00:00:00 0.28269 0.2750
## 4 36 Current 0.12528 0.0974
## 5 36 Current 0.24614 0.2085
## 6 60 Current 0.15425 0.1314
## LenderYield EstimatedEffectiveYield EstimatedLoss EstimatedReturn
## 1 0.1380 NA NA NA
## 2 0.0820 0.07960 0.0249 0.05470
## 3 0.2400 NA NA NA
## 4 0.0874 0.08490 0.0249 0.06000
## 5 0.1985 0.18316 0.0925 0.09066
## 6 0.1214 0.11567 0.0449 0.07077
## ProsperRating..numeric. ProsperRating..Alpha. ProsperScore
## 1 NA NA
## 2 6 A 7
## 3 NA NA
## 4 6 A 9
## 5 3 D 4
## 6 5 B 10
## ListingCategory..numeric. BorrowerState Occupation EmploymentStatus
## 1 0 CO Other Self-employed
## 2 2 CO Professional Employed
## 3 0 GA Other Not available
## 4 16 GA Skilled Labor Employed
## 5 2 MN Executive Employed
## 6 1 NM Professional Employed
## EmploymentStatusDuration IsBorrowerHomeowner CurrentlyInGroup
## 1 2 True True
## 2 44 False False
## 3 NA False True
## 4 113 True False
## 5 44 True False
## 6 82 True False
## GroupKey DateCreditPulled
## 1 2007-08-26 18:41:46.780000000
## 2 2014-02-27 08:28:14
## 3 783C3371218786870A73D20 2007-01-02 14:09:10.060000000
## 4 2012-10-22 11:02:32
## 5 2013-09-14 18:38:44
## 6 2013-12-14 08:26:40
## CreditScoreRangeLower CreditScoreRangeUpper FirstRecordedCreditLine
## 1 640 659 2001-10-11 00:00:00
## 2 680 699 1996-03-18 00:00:00
## 3 480 499 2002-07-27 00:00:00
## 4 800 819 1983-02-28 00:00:00
## 5 680 699 2004-02-20 00:00:00
## 6 740 759 1973-03-01 00:00:00
## CurrentCreditLines OpenCreditLines TotalCreditLinespast7years
## 1 5 4 12
## 2 14 14 29
## 3 NA NA 3
## 4 5 5 29
## 5 19 19 49
## 6 21 17 49
## OpenRevolvingAccounts OpenRevolvingMonthlyPayment InquiriesLast6Months
## 1 1 24 3
## 2 13 389 3
## 3 0 0 0
## 4 7 115 0
## 5 6 220 1
## 6 13 1410 0
## TotalInquiries CurrentDelinquencies AmountDelinquent
## 1 3 2 472
## 2 5 0 0
## 3 1 1 NA
## 4 1 4 10056
## 5 9 0 0
## 6 2 0 0
## DelinquenciesLast7Years PublicRecordsLast10Years
## 1 4 0
## 2 0 1
## 3 0 0
## 4 14 0
## 5 0 0
## 6 0 0
## PublicRecordsLast12Months RevolvingCreditBalance BankcardUtilization
## 1 0 0 0.00
## 2 0 3989 0.21
## 3 NA NA NA
## 4 0 1444 0.04
## 5 0 6193 0.81
## 6 0 62999 0.39
## AvailableBankcardCredit TotalTrades TradesNeverDelinquent..percentage.
## 1 1500 11 0.81
## 2 10266 29 1.00
## 3 NA NA NA
## 4 30754 26 0.76
## 5 695 39 0.95
## 6 86509 47 1.00
## TradesOpenedLast6Months DebtToIncomeRatio IncomeRange
## 1 0 0.17 $25,000-49,999
## 2 2 0.18 $50,000-74,999
## 3 NA 0.06 Not displayed
## 4 0 0.15 $25,000-49,999
## 5 2 0.26 $100,000+
## 6 0 0.36 $100,000+
## IncomeVerifiable StatedMonthlyIncome LoanKey
## 1 True 3083.333 E33A3400205839220442E84
## 2 True 6125.000 9E3B37071505919926B1D82
## 3 True 2083.333 6954337960046817851BCB2
## 4 True 2875.000 A0393664465886295619C51
## 5 True 9583.333 A180369302188889200689E
## 6 True 8333.333 C3D63702273952547E79520
## TotalProsperLoans TotalProsperPaymentsBilled OnTimeProsperPayments
## 1 NA NA NA
## 2 NA NA NA
## 3 NA NA NA
## 4 NA NA NA
## 5 1 11 11
## 6 NA NA NA
## ProsperPaymentsLessThanOneMonthLate ProsperPaymentsOneMonthPlusLate
## 1 NA NA
## 2 NA NA
## 3 NA NA
## 4 NA NA
## 5 0 0
## 6 NA NA
## ProsperPrincipalBorrowed ProsperPrincipalOutstanding
## 1 NA NA
## 2 NA NA
## 3 NA NA
## 4 NA NA
## 5 11000 9947.9
## 6 NA NA
## ScorexChangeAtTimeOfListing LoanCurrentDaysDelinquent
## 1 NA 0
## 2 NA 0
## 3 NA 0
## 4 NA 0
## 5 NA 0
## 6 NA 0
## LoanFirstDefaultedCycleNumber LoanMonthsSinceOrigination LoanNumber
## 1 NA 78 19141
## 2 NA 0 134815
## 3 NA 86 6466
## 4 NA 16 77296
## 5 NA 6 102670
## 6 NA 3 123257
## LoanOriginalAmount LoanOriginationDate LoanOriginationQuarter
## 1 9425 2007-09-12 00:00:00 Q3 2007
## 2 10000 2014-03-03 00:00:00 Q1 2014
## 3 3001 2007-01-17 00:00:00 Q1 2007
## 4 10000 2012-11-01 00:00:00 Q4 2012
## 5 15000 2013-09-20 00:00:00 Q3 2013
## 6 15000 2013-12-24 00:00:00 Q4 2013
## MemberKey MonthlyLoanPayment LP_CustomerPayments
## 1 1F3E3376408759268057EDA 330.43 11396.14
## 2 1D13370546739025387B2F4 318.93 0.00
## 3 5F7033715035555618FA612 123.32 4186.63
## 4 9ADE356069835475068C6D2 321.45 5143.20
## 5 36CE356043264555721F06C 563.97 2819.85
## 6 874A3701157341738DE458F 342.37 679.34
## LP_CustomerPrincipalPayments LP_InterestandFees LP_ServiceFees
## 1 9425.00 1971.14 -133.18
## 2 0.00 0.00 0.00
## 3 3001.00 1185.63 -24.20
## 4 4091.09 1052.11 -108.01
## 5 1563.22 1256.63 -60.27
## 6 351.89 327.45 -25.33
## LP_CollectionFees LP_GrossPrincipalLoss LP_NetPrincipalLoss
## 1 0 0 0
## 2 0 0 0
## 3 0 0 0
## 4 0 0 0
## 5 0 0 0
## 6 0 0 0
## LP_NonPrincipalRecoverypayments PercentFunded Recommendations
## 1 0 1 0
## 2 0 1 0
## 3 0 1 0
## 4 0 1 0
## 5 0 1 0
## 6 0 1 0
## InvestmentFromFriendsCount InvestmentFromFriendsAmount Investors
## 1 0 0 258
## 2 0 0 1
## 3 0 0 41
## 4 0 0 158
## 5 0 0 20
## 6 0 0 1Univariate Plots Section
We will be looking at a few variables that relate to both the loan itself (dollar amount, term) and the borrower (credit score, prosper rating) in order to determine what is likely to influence the total amount Prosper is willing to lend a borrower and at what rate.
Borrower Data Exploration: Subsection: Loan Original Amount
We will be examining the LoanOriginalAmount data from the loans dataset to better understand the frequency of loan values provided by Prosper.
head(sort(table(loans$LoanOriginalAmount), decreasing = T), 20)##
## 4000 15000 10000 5000 2000 3000 25000 20000 1000 2500 7500 7000
## 14333 12407 11106 6990 6067 5749 3630 3291 3206 2992 2975 2949
## 6000 3500 8000 12000 9000 13000 1500 4500
## 2869 2567 2442 1921 1695 1509 1507 1406summary(loans$LoanOriginalAmount)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 4000 6500 8337 12000 35000The table above shows that loans of 4,000 are the most provided by Propser. This value is below the median of 6500 and the Mean of 8337, which suggests there are some large loans that are pulling the mean forward.
The max loan provided by Prosper was 35,000.
qplot(data = loans, x = loans$LoanOriginalAmount, binwidth = 1000)+
geom_histogram()+
scale_x_continuous(breaks = seq(0,35000, 2000))+
ggtitle('Count of Loan Original Amount')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
The histogram above shows a spike at around 3,000- 4,000. This suggests there are a great number of loans provided in this area. Let’s examine further.
qplot(data = loans, x = loans$LoanOriginalAmount, binwidth = 500)+
geom_histogram()+
coord_cartesian(xlim = c(0,5000))+
scale_x_continuous(breaks = seq(0,5000, 1000))+
ggtitle('Count of Loan Original Amount by Binwidth = 500')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
head(sort(table(loans$LoanOriginalAmount), decreasing = T), 20)##
## 4000 15000 10000 5000 2000 3000 25000 20000 1000 2500 7500 7000
## 14333 12407 11106 6990 6067 5749 3630 3291 3206 2992 2975 2949
## 6000 3500 8000 12000 9000 13000 1500 4500
## 2869 2567 2442 1921 1695 1509 1507 1406Borrower Data Exploration: Subsection: Loan Term
Let’s look at the loan term provided by Prosper to get a sense of what types of loans and duration of loans Prosper gives to their borrowers.
sort(table(loans$Term))##
## 12 60 36
## 1614 24545 87778table(loans$Term)##
## 12 36 60
## 1614 87778 24545ggplot(data = loans, aes(x = loans$Term), binwidth = 1)+
geom_histogram()+
scale_x_continuous(breaks = seq(0,62,2))+
ggtitle('Count of loan terms')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
From the table and histogram above, we see that Prosper only gives loans in 12, 36, and 60 month terms. The majority of loans are provided on a 36 month term payment plan.
Borrower Data Exploration: Subsection: Amount Delinquent
We will examine the amount of money that is delinquent per borrower per Prosper loan.
DelinquenciesValues <- subset(loans, loans$AmountDelinquent != 0)
table(DelinquenciesValues$AmountDelinquent)##
## 1 2 3 4 5 6 7 8 9 10
## 7 10 7 6 9 9 5 6 7 30
## 11 12 13 14 15 16 17 18 19 20
## 8 9 12 12 34 6 12 6 8 30
## 21 22 23 24 25 26 27 28 29 30
## 8 11 8 12 66 14 15 19 15 65
## 31 32 33 34 35 36 37 38 39 40
## 22 24 27 20 29 25 22 12 14 43
## 41 42 43 44 45 46 47 48 49 50
## 15 22 21 18 26 19 21 24 15 73
## 51 52 53 54 55 56 57 58 59 60
## 25 24 23 26 34 21 25 17 17 46
## 61 62 63 64 65 66 67 68 69 70
## 17 18 18 22 34 22 32 25 13 29
## 71 72 73 74 75 76 77 78 79 80
## 22 17 11 20 56 21 17 23 26 28
## 81 82 83 84 85 86 87 88 89 90
## 19 19 15 24 18 19 18 25 13 25
## 91 92 93 94 95 96 97 98 99 100
## 13 15 22 22 16 12 20 21 13 67
## 101 102 103 104 105 106 107 108 109 110
## 23 19 21 16 25 19 21 17 13 26
## 111 112 113 114 115 116 117 118 119 120
## 14 21 19 19 23 20 17 16 15 35
## 121 122 123 124 125 126 127 128 129 130
## 13 12 16 13 18 13 11 11 22 31
## 131 132 133 134 135 136 137 138 139 140
## 15 20 14 25 21 7 9 19 9 19
## 141 142 143 144 145 146 147 148 149 150
## 11 13 14 10 18 12 16 11 13 32
## 151 152 153 154 155 156 157 158 159 160
## 14 15 21 11 9 13 11 23 7 15
## 161 162 163 164 165 166 167 168 169 170
## 15 14 9 13 10 17 18 12 9 10
## 171 172 173 174 175 176 177 178 179 180
## 13 14 9 18 17 11 7 20 14 15
## 181 182 183 184 185 186 187 188 189 190
## 12 12 14 9 21 9 8 10 13 9
## 191 192 193 194 195 196 197 198 199 200
## 16 13 9 10 10 8 11 9 9 29
## 201 202 203 204 205 206 207 208 209 210
## 11 16 12 7 7 15 13 7 14 14
## 211 212 213 214 215 216 217 218 219 220
## 10 8 12 18 7 9 9 9 9 18
## 221 222 223 224 225 226 227 228 229 230
## 9 6 20 13 15 8 13 20 12 24
## 231 232 233 234 235 236 237 238 239 240
## 13 9 9 13 9 9 5 9 10 8
## 241 242 243 244 245 246 247 248 249 250
## 9 6 9 8 13 13 10 15 10 20
## 251 252 253 254 255 256 257 258 259 260
## 10 11 13 13 12 9 13 15 14 12
## 261 262 263 264 265 266 267 268 269 270
## 7 9 9 9 10 13 14 7 19 9
## 271 272 273 274 275 276 277 278 279 280
## 7 5 10 10 7 11 7 10 18 15
## 281 282 283 284 285 286 287 288 289 290
## 12 4 12 12 14 11 6 9 8 12
## 291 292 293 294 295 296 297 298 299 300
## 9 9 8 12 14 14 10 11 10 26
## 301 302 303 304 305 306 307 308 309 310
## 10 8 5 8 5 11 10 12 6 8
## 311 312 313 314 315 316 317 318 319 320
## 8 4 11 8 10 13 4 10 9 11
## 321 322 323 324 325 326 327 328 329 330
## 4 7 4 7 9 5 9 3 3 11
## 331 332 333 334 335 336 337 338 339 340
## 6 8 2 4 4 10 10 8 4 8
## 341 342 343 344 345 346 347 348 349 350
## 7 7 7 8 2 6 3 10 10 23
## 351 352 353 354 355 356 357 358 359 360
## 7 12 12 3 9 8 10 11 6 10
## 361 362 363 364 365 366 367 368 369 370
## 6 4 11 5 7 8 10 14 8 15
## 371 372 373 374 375 376 377 378 379 380
## 5 9 2 5 8 5 7 9 10 10
## 381 382 383 384 385 386 387 388 389 390
## 9 11 9 3 7 8 7 7 6 9
## 391 392 393 394 395 396 397 398 399 400
## 6 6 9 4 6 6 5 8 3 16
## 401 402 403 404 405 406 407 408 409 410
## 11 8 15 4 7 2 4 7 8 6
## 411 412 413 414 415 416 417 418 419 420
## 7 7 6 5 4 9 8 5 6 7
## 421 422 423 424 425 426 427 428 429 430
## 4 6 7 6 8 9 6 9 7 5
## 431 432 433 434 435 436 437 438 439 440
## 8 4 16 3 3 7 4 10 5 7
## 441 442 443 444 445 446 447 448 449 450
## 5 2 4 5 2 9 10 8 4 12
## 451 452 453 454 455 456 457 458 459 460
## 5 3 2 7 4 4 10 6 6 15
## 461 463 464 465 466 467 468 469 470 471
## 6 8 2 5 4 4 7 5 4 3
## 472 473 474 475 476 477 478 479 480 481
## 7 2 7 10 9 5 8 8 6 3
## 482 483 484 485 486 487 488 489 490 491
## 10 5 4 5 9 2 4 4 10 6
## 492 493 494 495 496 497 498 499 500 501
## 3 3 9 13 6 8 5 6 11 4
## 502 503 504 505 506 507 508 509 510 511
## 7 4 6 5 8 2 7 2 8 5
## 512 513 514 515 516 517 518 519 520 521
## 7 4 8 7 1 2 9 4 7 5
## 522 523 524 525 526 527 528 529 530 531
## 5 3 1 11 8 5 4 5 5 4
## 532 533 534 535 536 537 538 539 540 541
## 6 6 10 8 10 2 5 5 5 6
## 542 543 544 545 546 547 548 549 550 551
## 5 8 2 5 6 6 7 6 7 4
## 552 553 554 555 556 557 558 559 560 561
## 7 7 3 4 3 4 2 4 8 7
## 562 563 564 565 566 567 568 569 570 571
## 2 3 2 3 7 7 6 6 8 5
## 572 573 574 575 576 577 578 579 580 581
## 6 3 3 3 4 8 4 6 3 2
## 582 583 584 585 586 587 588 589 590 591
## 4 5 6 3 4 8 2 6 11 8
## 592 593 594 595 596 597 598 599 600 601
## 3 2 1 7 8 7 5 4 17 3
## 602 603 604 605 606 607 608 609 610 611
## 3 8 2 4 2 3 5 8 6 7
## 612 613 614 615 616 617 618 619 620 621
## 2 6 5 4 4 4 7 10 7 2
## 622 623 624 625 626 627 628 630 631 632
## 3 5 6 2 4 4 3 10 3 5
## 633 634 635 636 637 638 639 640 641 642
## 9 2 5 2 7 5 3 5 7 5
## 643 644 645 646 647 648 649 650 651 652
## 4 10 4 3 5 9 2 12 2 3
## 653 654 655 656 657 658 659 660 661 662
## 3 6 4 8 6 5 5 7 5 6
## 663 664 665 666 667 668 669 670 671 672
## 3 7 2 11 4 4 3 2 11 5
## 673 674 675 676 677 678 679 680 681 682
## 4 3 5 3 7 5 3 3 2 2
## 683 684 686 687 688 689 690 691 692 693
## 5 2 10 2 3 6 3 6 8 5
## 694 695 696 697 698 699 700 701 702 703
## 9 4 2 1 6 1 10 2 2 5
## 704 705 706 707 708 709 710 711 712 713
## 3 1 7 6 5 2 6 5 4 5
## 714 715 716 717 718 719 720 721 722 723
## 2 6 3 1 2 4 4 4 4 5
## 724 725 726 727 728 729 730 731 732 733
## 3 7 9 3 4 2 2 4 2 3
## 734 735 736 737 738 739 740 741 742 743
## 1 4 6 4 1 5 5 1 2 2
## 744 745 746 747 748 749 750 751 752 753
## 3 1 2 1 5 1 10 8 6 5
## 754 755 756 757 758 759 760 761 762 763
## 5 7 2 4 6 2 3 4 4 2
## 764 765 766 767 768 769 770 771 772 773
## 4 7 3 4 2 2 7 3 7 5
## 774 775 776 777 778 779 780 781 782 783
## 3 6 5 4 2 2 3 1 3 4
## 784 785 786 787 788 789 790 791 793 795
## 5 3 1 5 1 3 2 8 2 3
## 796 797 798 799 800 801 802 803 804 805
## 2 2 1 2 7 1 2 2 8 7
## 806 807 808 809 810 811 812 813 814 815
## 3 2 2 5 5 1 1 1 7 5
## 816 817 818 819 820 821 822 823 824 825
## 2 2 3 2 4 2 5 3 2 1
## 826 827 828 829 830 831 832 833 834 835
## 1 1 1 5 4 1 4 1 4 4
## 836 837 838 839 840 841 842 843 844 845
## 2 3 3 3 5 3 7 1 2 7
## 846 847 848 849 850 851 852 853 854 855
## 4 1 3 3 6 4 2 3 2 7
## 856 857 858 859 860 861 862 863 864 865
## 3 2 2 3 1 5 6 1 6 3
## 866 867 868 869 870 872 873 874 875 876
## 2 1 2 4 6 4 3 3 5 5
## 877 878 879 880 881 882 883 884 885 886
## 2 1 3 5 2 3 3 4 3 5
## 887 888 889 890 891 892 893 894 895 896
## 8 2 1 6 3 2 4 2 6 3
## 897 898 899 900 902 903 904 905 906 907
## 3 5 1 4 4 2 3 4 2 2
## 908 909 910 912 913 914 915 916 917 918
## 1 2 1 5 2 1 2 2 7 4
## 919 920 921 922 923 924 925 926 927 928
## 3 1 2 3 2 3 2 3 4 3
## 929 930 931 932 933 934 935 936 937 938
## 1 2 7 6 2 5 1 5 2 4
## 939 940 941 942 943 944 945 946 947 948
## 2 2 3 2 2 1 2 4 3 2
## 949 951 952 953 954 955 957 959 960 961
## 4 3 3 1 2 2 2 5 5 2
## 962 963 965 966 969 970 971 972 973 974
## 2 1 1 1 4 1 4 3 1 1
## 975 976 977 978 979 980 982 983 984 985
## 2 7 3 2 1 3 2 2 2 3
## 986 987 988 989 990 991 992 993 994 995
## 1 1 2 2 1 1 5 2 4 4
## 996 997 998 999 1000 1001 1002 1003 1004 1005
## 4 3 5 1 2 4 4 5 4 2
## 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015
## 3 1 3 2 6 7 3 3 3 1
## 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025
## 4 2 4 1 1 3 1 3 4 2
## 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
## 6 2 3 3 1 2 3 1 3 3
## 1037 1038 1039 1040 1042 1043 1044 1046 1047 1048
## 2 1 4 1 2 1 3 1 3 2
## 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058
## 2 3 1 2 1 3 2 5 2 3
## 1059 1060 1061 1062 1063 1064 1066 1067 1068 1069
## 2 3 3 3 1 4 6 4 2 2
## 1070 1071 1072 1073 1074 1075 1077 1078 1079 1080
## 3 4 3 4 4 2 2 4 1 2
## 1081 1082 1083 1084 1086 1087 1088 1089 1090 1091
## 1 3 1 7 1 3 2 1 5 4
## 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101
## 2 1 6 6 3 2 2 3 2 2
## 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111
## 5 5 3 6 1 4 5 2 5 2
## 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121
## 5 1 1 3 3 2 2 6 1 4
## 1122 1123 1124 1125 1126 1127 1129 1130 1132 1133
## 3 1 3 2 6 4 3 4 3 3
## 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143
## 3 1 3 4 2 2 6 1 5 2
## 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153
## 2 1 3 1 4 1 2 1 2 1
## 1154 1155 1156 1157 1159 1160 1161 1162 1164 1165
## 2 8 5 1 2 3 3 3 4 3
## 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175
## 4 1 1 1 2 4 5 2 5 5
## 1176 1177 1178 1179 1180 1181 1183 1184 1185 1186
## 3 3 5 3 5 5 4 1 1 3
## 1187 1188 1189 1190 1192 1195 1196 1197 1198 1199
## 2 4 2 1 5 1 2 2 1 3
## 1200 1201 1202 1203 1205 1206 1207 1208 1209 1210
## 2 3 3 1 4 1 7 1 1 3
## 1211 1212 1213 1214 1215 1217 1218 1219 1220 1223
## 3 7 1 4 3 3 3 4 3 1
## 1224 1225 1226 1227 1228 1229 1231 1232 1233 1234
## 3 3 1 6 3 5 1 2 3 7
## 1235 1236 1238 1241 1242 1243 1244 1245 1246 1247
## 4 2 4 2 3 2 2 4 2 5
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## 18674 18678 18686 18698 18718 18720 18723 18729 18737 18747
## 5 2 1 1 1 1 1 1 1 1
## 18822 18839 18854 18859 18861 18866 18893 18908 18929 18930
## 1 1 1 1 1 1 1 1 1 2
## 18932 18971 18978 18983 18986 18992 18998 19014 19018 19038
## 1 1 2 1 1 1 1 1 1 1
## 19053 19063 19090 19100 19104 19108 19135 19145 19156 19163
## 1 1 1 1 1 1 1 1 1 1
## 19165 19172 19193 19212 19226 19260 19263 19268 19277 19302
## 1 1 2 1 1 3 1 1 1 2
## 19315 19321 19328 19341 19349 19369 19401 19403 19435 19453
## 1 2 1 1 1 1 1 1 1 1
## 19458 19460 19474 19498 19501 19541 19584 19589 19608 19612
## 1 1 1 1 1 1 1 1 1 1
## 19638 19641 19659 19664 19681 19685 19688 19690 19695 19704
## 1 1 1 2 1 1 1 1 1 1
## 19707 19710 19722 19725 19726 19738 19754 19756 19772 19773
## 1 1 2 1 1 1 1 1 1 1
## 19779 19796 19849 19861 19869 19890 19911 19923 19963 20012
## 1 1 1 1 1 1 1 1 1 1
## 20058 20067 20095 20100 20107 20112 20118 20128 20135 20149
## 1 1 1 1 1 1 1 1 1 1
## 20150 20164 20172 20185 20207 20210 20218 20235 20241 20285
## 1 1 1 1 1 1 1 1 1 1
## 20286 20328 20348 20349 20373 20469 20472 20503 20510 20533
## 1 1 1 1 1 1 1 1 1 2
## 20542 20589 20604 20641 20647 20657 20664 20674 20681 20700
## 1 1 1 1 2 1 1 1 1 1
## 20729 20730 20763 20779 20785 20811 20851 20869 20874 20886
## 1 1 1 1 1 1 1 1 1 1
## 20907 20911 20928 20944 20965 20979 20990 21009 21018 21019
## 1 1 1 1 1 1 2 1 1 1
## 21026 21042 21060 21126 21135 21139 21147 21149 21157 21166
## 1 1 1 1 3 1 1 1 3 1
## 21195 21216 21251 21266 21276 21285 21297 21299 21323 21350
## 1 1 1 1 1 1 1 1 1 1
## 21369 21393 21400 21404 21446 21460 21465 21500 21505 21541
## 1 2 1 1 1 1 1 1 1 1
## 21567 21615 21618 21628 21636 21659 21691 21723 21751 21758
## 1 1 1 1 1 1 1 1 1 1
## 21783 21844 21858 21891 21893 21904 21905 21909 21928 21944
## 1 1 1 1 1 1 1 1 1 1
## 21969 21972 21980 21989 22010 22049 22058 22091 22093 22115
## 1 1 1 1 1 1 1 1 1 1
## 22144 22155 22165 22169 22174 22177 22187 22221 22228 22245
## 1 1 1 1 1 1 1 1 1 1
## 22264 22271 22273 22284 22291 22307 22332 22397 22431 22435
## 1 1 1 2 1 1 1 1 1 1
## 22449 22495 22502 22526 22529 22555 22578 22624 22668 22674
## 1 1 1 1 1 1 1 1 1 1
## 22682 22697 22713 22754 22757 22775 22776 22793 22831 22855
## 1 2 1 1 1 1 1 1 1 2
## 22871 22882 22889 22903 22922 22925 22929 22947 22963 22969
## 1 1 1 1 1 1 1 1 1 1
## 22994 23029 23034 23044 23057 23064 23066 23096 23100 23102
## 1 1 1 2 1 1 1 4 3 1
## 23107 23109 23129 23189 23210 23251 23254 23262 23302 23308
## 1 1 1 1 1 1 1 1 1 1
## 23320 23368 23415 23423 23472 23473 23476 23505 23511 23535
## 1 1 1 1 1 1 1 1 2 1
## 23549 23552 23562 23571 23601 23610 23626 23630 23644 23650
## 1 1 1 1 1 1 3 1 1 1
## 23660 23668 23671 23676 23727 23740 23748 23752 23754 23756
## 2 1 1 1 1 1 1 1 1 2
## 23759 23772 23802 23835 23867 23880 23931 23960 23973 23983
## 1 1 1 1 1 1 1 1 1 1
## 23984 24008 24012 24024 24026 24046 24050 24070 24072 24089
## 1 1 1 1 1 1 1 1 1 1
## 24096 24099 24115 24132 24150 24173 24177 24184 24199 24237
## 1 1 2 1 1 1 1 1 1 1
## 24251 24270 24280 24291 24297 24350 24351 24364 24400 24413
## 1 2 1 1 1 1 2 1 1 1
## 24442 24444 24476 24512 24589 24592 24614 24632 24642 24665
## 1 1 2 1 1 1 1 1 1 1
## 24675 24677 24701 24762 24763 24802 24808 24831 24850 24858
## 1 1 1 1 1 2 1 1 1 1
## 24865 24871 24910 24940 24975 24981 24998 25000 25018 25045
## 1 1 1 1 1 1 1 1 1 1
## 25054 25067 25108 25119 25133 25153 25166 25170 25218 25224
## 1 1 1 1 1 1 1 1 1 1
## 25255 25257 25270 25274 25280 25307 25320 25360 25389 25392
## 1 1 1 1 1 1 1 1 2 1
## 25464 25476 25500 25512 25579 25589 25611 25623 25627 25645
## 1 1 1 1 1 1 1 1 1 1
## 25651 25662 25664 25730 25735 25766 25781 25784 25911 25928
## 1 1 1 1 1 2 1 1 1 1
## 25980 26017 26043 26057 26070 26085 26098 26107 26124 26172
## 1 1 1 1 1 1 1 1 1 1
## 26175 26231 26331 26403 26412 26436 26450 26487 26536 26593
## 2 1 1 1 1 1 1 1 1 1
## 26600 26601 26622 26623 26673 26679 26704 26752 26795 26811
## 1 1 1 1 2 1 1 1 1 1
## 26813 26815 26818 26836 26838 26843 26931 26955 26978 26987
## 1 1 1 1 1 1 1 1 1 1
## 26989 27011 27021 27031 27060 27065 27075 27090 27098 27106
## 1 1 1 1 1 1 1 1 1 1
## 27129 27136 27150 27198 27311 27367 27400 27404 27460 27466
## 2 1 1 1 1 1 1 1 1 2
## 27491 27528 27551 27558 27649 27651 27663 27719 27755 27784
## 1 1 1 1 1 1 1 1 1 1
## 27787 27870 27883 27898 27927 27969 27997 28014 28034 28057
## 1 1 1 1 1 1 1 1 1 1
## 28065 28070 28094 28114 28125 28133 28147 28172 28174 28175
## 1 1 1 1 1 1 1 1 1 1
## 28200 28247 28255 28260 28277 28389 28410 28433 28463 28464
## 1 2 1 1 1 1 1 1 1 1
## 28473 28502 28504 28505 28587 28591 28600 28649 28667 28681
## 1 1 1 1 1 2 1 1 1 1
## 28684 28740 28782 28840 28929 28963 29072 29074 29082 29119
## 1 1 1 1 1 1 2 1 1 1
## 29140 29156 29183 29207 29246 29285 29319 29335 29369 29375
## 1 1 1 1 1 1 1 1 1 1
## 29403 29429 29446 29448 29487 29489 29537 29687 29688 29719
## 1 1 1 1 1 1 1 1 1 1
## 29776 29795 29809 29875 29876 29882 29997 30023 30027 30097
## 1 2 1 1 1 1 1 1 1 1
## 30112 30119 30202 30231 30239 30347 30402 30408 30417 30441
## 1 1 1 1 1 1 1 1 1 1
## 30453 30500 30520 30563 30579 30588 30645 30664 30667 30682
## 1 1 1 1 1 1 1 1 1 1
## 30691 30747 30777 30803 30920 30928 30948 30970 30997 30998
## 1 1 1 1 1 1 1 1 1 1
## 31013 31031 31035 31041 31099 31115 31176 31251 31297 31348
## 1 1 1 1 1 1 1 1 1 1
## 31352 31392 31404 31497 31533 31541 31550 31605 31622 31631
## 1 1 1 1 1 1 1 1 1 1
## 31761 31847 31894 31913 31919 32005 32006 32069 32110 32119
## 1 1 1 1 1 1 1 1 1 1
## 32138 32175 32200 32254 32326 32390 32396 32413 32497 32500
## 1 1 1 1 1 1 1 1 1 1
## 32576 32645 32683 32698 32755 32766 32790 32859 32946 32961
## 1 1 1 1 1 1 1 1 1 1
## 32969 33036 33057 33134 33135 33154 33240 33323 33324 33337
## 3 1 1 1 1 2 1 1 1 1
## 33376 33432 33463 33506 33509 33520 33555 33566 33628 33646
## 1 1 1 1 1 1 1 1 1 1
## 33773 33783 33801 33803 33835 33852 33863 33888 33925 33929
## 1 1 1 1 1 1 1 1 1 1
## 33998 34133 34171 34183 34193 34225 34336 34381 34388 34416
## 1 1 1 1 1 1 1 1 1 1
## 34434 34435 34525 34555 34645 34666 34794 34836 34874 34876
## 1 1 1 1 1 1 1 1 2 1
## 34880 34899 34911 34968 34977 34988 34990 34997 35008 35055
## 1 2 1 1 1 1 1 1 1 1
## 35096 35097 35119 35128 35169 35185 35212 35227 35250 35299
## 1 1 1 1 1 1 1 1 1 1
## 35334 35374 35454 35457 35459 35471 35514 35574 35727 35794
## 1 1 1 1 1 1 1 1 3 1
## 35849 35901 35927 35972 36153 36302 36363 36384 36471 36477
## 2 1 1 1 1 1 1 1 1 1
## 36492 36514 36598 36626 36863 36961 37003 37077 37212 37287
## 1 1 1 1 1 1 1 1 1 1
## 37291 37316 37317 37329 37339 37454 37463 37534 37642 37643
## 1 1 1 1 1 2 1 1 1 1
## 37655 37837 37855 37919 37936 37998 38068 38108 38149 38160
## 1 1 1 1 1 1 1 1 1 1
## 38212 38286 38304 38336 38365 38417 38432 38475 38489 38657
## 1 1 1 1 1 1 1 1 1 1
## 38660 38664 38665 38709 38870 38960 38996 39011 39028 39210
## 3 1 1 1 1 1 1 1 1 1
## 39227 39295 39379 39409 39470 39473 39484 39632 39856 39986
## 1 1 1 1 1 1 1 1 1 1
## 40013 40087 40189 40335 40389 40392 40482 40485 40527 40553
## 1 2 1 1 1 1 1 1 1 1
## 40633 40779 40836 40938 41014 41020 41214 41244 41361 41374
## 1 2 1 1 1 4 1 1 1 1
## 41378 41386 41661 41694 41763 41822 41975 42205 42342 42370
## 1 1 1 1 1 1 1 1 1 1
## 42387 42485 42488 42556 42824 42854 42881 42962 43064 43079
## 1 1 1 1 1 1 1 1 1 1
## 43093 43121 43200 43322 43363 43367 43437 43607 43642 43722
## 1 1 1 1 1 1 1 1 1 1
## 43761 43776 43789 43958 44036 44203 44262 44307 44369 44493
## 1 1 1 1 1 1 1 1 1 1
## 44734 44744 44859 44879 45059 45201 45202 45298 45364 45655
## 1 1 1 1 1 1 1 1 1 1
## 45726 45857 45864 45979 46010 46065 46099 46127 46216 46255
## 1 1 1 1 1 1 1 1 2 1
## 46331 46359 46394 46642 46943 46989 47008 47371 47625 47746
## 1 1 1 1 1 1 1 1 1 1
## 47766 47918 47963 47965 48009 48024 48100 48121 48150 48201
## 1 1 1 1 1 1 1 1 2 1
## 48289 48423 48487 48673 48703 48865 48992 49047 49116 49178
## 1 1 1 2 1 1 1 1 1 1
## 49229 49248 49274 49283 49454 49466 49759 49809 49818 49868
## 1 1 1 1 1 1 1 1 1 1
## 49924 50017 50163 50261 50385 50396 50421 50610 50688 50852
## 1 1 1 1 1 1 1 1 1 1
## 51103 51119 51252 51344 51370 51788 51847 52033 52047 52379
## 1 1 1 1 1 1 1 1 1 1
## 52456 52480 52612 52820 52844 53054 53083 53148 53215 53335
## 1 1 1 1 1 1 1 1 1 1
## 53351 53420 53439 53442 53622 53798 53824 54000 54007 54068
## 1 1 1 1 1 1 1 1 1 1
## 54364 54480 54550 54596 54782 54881 54915 54918 55111 55462
## 1 1 1 1 1 1 1 1 1 1
## 55716 55869 55958 56254 56288 56502 56716 56743 57252 57265
## 1 1 1 1 1 1 1 1 1 1
## 57376 57580 57884 57979 58221 58365 58463 58521 58565 58583
## 1 1 1 1 1 1 1 1 1 1
## 58678 58708 58858 59241 59415 59613 59692 59860 59883 60170
## 1 1 1 1 1 1 2 1 1 1
## 60308 60310 60346 60433 60510 60571 60616 60966 60997 61085
## 1 1 1 1 1 1 1 1 1 1
## 61231 61350 61393 61442 61564 61635 61745 61821 61981 62092
## 1 1 1 1 1 1 1 1 1 1
## 62129 62259 62312 62348 62512 62891 62903 63047 63217 63290
## 1 1 1 1 1 1 1 1 1 1
## 63373 63482 63558 63743 63897 64116 64420 64519 64538 64587
## 1 1 1 2 1 1 1 1 1 1
## 64595 64839 64868 65216 65320 65938 65951 65959 66422 66466
## 1 1 1 1 1 1 1 1 1 1
## 66600 66852 67434 67449 68013 68123 68304 68587 68828 68900
## 1 1 1 1 1 2 1 1 1 1
## 69276 69313 69483 69551 69823 69875 69907 70000 70132 70146
## 1 1 1 1 1 1 1 1 1 1
## 70334 70456 70567 70659 70734 70983 71328 72051 72112 72113
## 1 1 1 5 1 1 1 1 1 1
## 72121 72156 72302 72313 72705 72817 72997 73118 73323 73490
## 1 1 1 1 1 1 1 1 1 1
## 73661 73936 74579 74844 74990 75492 76008 76588 76840 77300
## 1 2 2 1 1 1 1 1 1 1
## 77384 77422 77771 77853 77985 78097 78380 78750 78935 79522
## 1 1 1 1 1 1 1 1 1 1
## 79574 80097 80346 80441 80646 80792 80975 81004 81495 81723
## 1 1 1 1 1 1 1 1 1 1
## 82271 82580 82708 82980 83138 83534 83756 83956 84427 84691
## 1 1 1 1 1 1 1 1 1 1
## 84834 84933 85065 85803 85885 85953 86101 86127 86282 86303
## 1 1 1 1 1 1 1 1 1 1
## 86351 86566 86730 87588 89000 89265 89523 89827 90536 90588
## 2 1 1 1 1 1 1 1 1 1
## 90756 91162 91501 91554 91636 91687 92177 92467 92753 93237
## 1 1 1 1 1 1 2 1 1 1
## 93593 95043 95280 95320 95389 95441 97020 97773 99792 99979
## 1 1 1 1 1 1 1 1 1 1
## 99991 101212 101497 101512 101644 102546 102936 102959 103076 103505
## 2 1 1 1 1 1 1 2 1 1
## 103709 103884 103975 104768 105340 105575 106071 106156 107319 107354
## 1 1 1 1 1 1 2 1 1 1
## 108415 109820 109956 110541 111524 111690 111873 112221 112684 113205
## 1 1 1 1 1 1 1 1 1 1
## 113552 114385 114872 116014 116896 117937 119147 119660 120153 120642
## 1 1 1 1 1 1 1 1 1 1
## 121379 122690 122868 123828 123871 124318 124471 124651 124691 124858
## 1 1 1 1 1 1 1 2 1 1
## 124888 126638 126830 127058 127472 127850 128639 128864 128993 129746
## 1 1 1 1 1 1 2 1 1 1
## 130093 131214 134322 135229 136476 142263 143329 144886 145618 149901
## 1 1 1 3 1 1 1 1 2 1
## 153237 155578 157422 158486 160039 161344 161475 161782 164607 165097
## 1 1 1 1 1 1 1 1 1 1
## 168648 171093 172240 173334 174862 175281 176347 179158 183396 188818
## 1 1 1 1 1 1 1 1 1 1
## 190585 192016 202741 205400 215315 223738 225595 230291 241707 242333
## 1 1 1 1 1 1 1 1 1 1
## 249209 255963 265084 279970 284169 327677 444745 463881
## 1 1 1 1 1 1 1 1ggplot(data = DelinquenciesValues, aes(x = AmountDelinquent))+
geom_histogram()+
ggtitle('Count of Amount Delinquent')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
summary(loans$AmountDelinquent)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.0 0.0 0.0 984.5 0.0 463881.0 7622head(sort(table(loans$AmountDelinquent), decreasing = TRUE), 50)##
## 0 50 100 25 30 75 60 40 120 15 55 65
## 89818 73 67 66 65 56 46 43 35 34 34 34
## 67 150 130 10 20 35 70 200 80 33 45 54
## 32 32 31 30 30 29 29 29 28 27 26 26
## 79 110 300 36 51 57 68 88 90 105 134 32
## 26 26 26 25 25 25 25 25 25 25 25 24
## 48 52 84 230 53 78 101 115 158 350 31 37
## 24 24 24 24 23 23 23 23 23 23 22 22
## 42 64
## 22 22DelinquenciesValues <- subset(loans, loans$AmountDelinquent != 0)
table(DelinquenciesValues$AmountDelinquent)##
## 1 2 3 4 5 6 7 8 9 10
## 7 10 7 6 9 9 5 6 7 30
## 11 12 13 14 15 16 17 18 19 20
## 8 9 12 12 34 6 12 6 8 30
## 21 22 23 24 25 26 27 28 29 30
## 8 11 8 12 66 14 15 19 15 65
## 31 32 33 34 35 36 37 38 39 40
## 22 24 27 20 29 25 22 12 14 43
## 41 42 43 44 45 46 47 48 49 50
## 15 22 21 18 26 19 21 24 15 73
## 51 52 53 54 55 56 57 58 59 60
## 25 24 23 26 34 21 25 17 17 46
## 61 62 63 64 65 66 67 68 69 70
## 17 18 18 22 34 22 32 25 13 29
## 71 72 73 74 75 76 77 78 79 80
## 22 17 11 20 56 21 17 23 26 28
## 81 82 83 84 85 86 87 88 89 90
## 19 19 15 24 18 19 18 25 13 25
## 91 92 93 94 95 96 97 98 99 100
## 13 15 22 22 16 12 20 21 13 67
## 101 102 103 104 105 106 107 108 109 110
## 23 19 21 16 25 19 21 17 13 26
## 111 112 113 114 115 116 117 118 119 120
## 14 21 19 19 23 20 17 16 15 35
## 121 122 123 124 125 126 127 128 129 130
## 13 12 16 13 18 13 11 11 22 31
## 131 132 133 134 135 136 137 138 139 140
## 15 20 14 25 21 7 9 19 9 19
## 141 142 143 144 145 146 147 148 149 150
## 11 13 14 10 18 12 16 11 13 32
## 151 152 153 154 155 156 157 158 159 160
## 14 15 21 11 9 13 11 23 7 15
## 161 162 163 164 165 166 167 168 169 170
## 15 14 9 13 10 17 18 12 9 10
## 171 172 173 174 175 176 177 178 179 180
## 13 14 9 18 17 11 7 20 14 15
## 181 182 183 184 185 186 187 188 189 190
## 12 12 14 9 21 9 8 10 13 9
## 191 192 193 194 195 196 197 198 199 200
## 16 13 9 10 10 8 11 9 9 29
## 201 202 203 204 205 206 207 208 209 210
## 11 16 12 7 7 15 13 7 14 14
## 211 212 213 214 215 216 217 218 219 220
## 10 8 12 18 7 9 9 9 9 18
## 221 222 223 224 225 226 227 228 229 230
## 9 6 20 13 15 8 13 20 12 24
## 231 232 233 234 235 236 237 238 239 240
## 13 9 9 13 9 9 5 9 10 8
## 241 242 243 244 245 246 247 248 249 250
## 9 6 9 8 13 13 10 15 10 20
## 251 252 253 254 255 256 257 258 259 260
## 10 11 13 13 12 9 13 15 14 12
## 261 262 263 264 265 266 267 268 269 270
## 7 9 9 9 10 13 14 7 19 9
## 271 272 273 274 275 276 277 278 279 280
## 7 5 10 10 7 11 7 10 18 15
## 281 282 283 284 285 286 287 288 289 290
## 12 4 12 12 14 11 6 9 8 12
## 291 292 293 294 295 296 297 298 299 300
## 9 9 8 12 14 14 10 11 10 26
## 301 302 303 304 305 306 307 308 309 310
## 10 8 5 8 5 11 10 12 6 8
## 311 312 313 314 315 316 317 318 319 320
## 8 4 11 8 10 13 4 10 9 11
## 321 322 323 324 325 326 327 328 329 330
## 4 7 4 7 9 5 9 3 3 11
## 331 332 333 334 335 336 337 338 339 340
## 6 8 2 4 4 10 10 8 4 8
## 341 342 343 344 345 346 347 348 349 350
## 7 7 7 8 2 6 3 10 10 23
## 351 352 353 354 355 356 357 358 359 360
## 7 12 12 3 9 8 10 11 6 10
## 361 362 363 364 365 366 367 368 369 370
## 6 4 11 5 7 8 10 14 8 15
## 371 372 373 374 375 376 377 378 379 380
## 5 9 2 5 8 5 7 9 10 10
## 381 382 383 384 385 386 387 388 389 390
## 9 11 9 3 7 8 7 7 6 9
## 391 392 393 394 395 396 397 398 399 400
## 6 6 9 4 6 6 5 8 3 16
## 401 402 403 404 405 406 407 408 409 410
## 11 8 15 4 7 2 4 7 8 6
## 411 412 413 414 415 416 417 418 419 420
## 7 7 6 5 4 9 8 5 6 7
## 421 422 423 424 425 426 427 428 429 430
## 4 6 7 6 8 9 6 9 7 5
## 431 432 433 434 435 436 437 438 439 440
## 8 4 16 3 3 7 4 10 5 7
## 441 442 443 444 445 446 447 448 449 450
## 5 2 4 5 2 9 10 8 4 12
## 451 452 453 454 455 456 457 458 459 460
## 5 3 2 7 4 4 10 6 6 15
## 461 463 464 465 466 467 468 469 470 471
## 6 8 2 5 4 4 7 5 4 3
## 472 473 474 475 476 477 478 479 480 481
## 7 2 7 10 9 5 8 8 6 3
## 482 483 484 485 486 487 488 489 490 491
## 10 5 4 5 9 2 4 4 10 6
## 492 493 494 495 496 497 498 499 500 501
## 3 3 9 13 6 8 5 6 11 4
## 502 503 504 505 506 507 508 509 510 511
## 7 4 6 5 8 2 7 2 8 5
## 512 513 514 515 516 517 518 519 520 521
## 7 4 8 7 1 2 9 4 7 5
## 522 523 524 525 526 527 528 529 530 531
## 5 3 1 11 8 5 4 5 5 4
## 532 533 534 535 536 537 538 539 540 541
## 6 6 10 8 10 2 5 5 5 6
## 542 543 544 545 546 547 548 549 550 551
## 5 8 2 5 6 6 7 6 7 4
## 552 553 554 555 556 557 558 559 560 561
## 7 7 3 4 3 4 2 4 8 7
## 562 563 564 565 566 567 568 569 570 571
## 2 3 2 3 7 7 6 6 8 5
## 572 573 574 575 576 577 578 579 580 581
## 6 3 3 3 4 8 4 6 3 2
## 582 583 584 585 586 587 588 589 590 591
## 4 5 6 3 4 8 2 6 11 8
## 592 593 594 595 596 597 598 599 600 601
## 3 2 1 7 8 7 5 4 17 3
## 602 603 604 605 606 607 608 609 610 611
## 3 8 2 4 2 3 5 8 6 7
## 612 613 614 615 616 617 618 619 620 621
## 2 6 5 4 4 4 7 10 7 2
## 622 623 624 625 626 627 628 630 631 632
## 3 5 6 2 4 4 3 10 3 5
## 633 634 635 636 637 638 639 640 641 642
## 9 2 5 2 7 5 3 5 7 5
## 643 644 645 646 647 648 649 650 651 652
## 4 10 4 3 5 9 2 12 2 3
## 653 654 655 656 657 658 659 660 661 662
## 3 6 4 8 6 5 5 7 5 6
## 663 664 665 666 667 668 669 670 671 672
## 3 7 2 11 4 4 3 2 11 5
## 673 674 675 676 677 678 679 680 681 682
## 4 3 5 3 7 5 3 3 2 2
## 683 684 686 687 688 689 690 691 692 693
## 5 2 10 2 3 6 3 6 8 5
## 694 695 696 697 698 699 700 701 702 703
## 9 4 2 1 6 1 10 2 2 5
## 704 705 706 707 708 709 710 711 712 713
## 3 1 7 6 5 2 6 5 4 5
## 714 715 716 717 718 719 720 721 722 723
## 2 6 3 1 2 4 4 4 4 5
## 724 725 726 727 728 729 730 731 732 733
## 3 7 9 3 4 2 2 4 2 3
## 734 735 736 737 738 739 740 741 742 743
## 1 4 6 4 1 5 5 1 2 2
## 744 745 746 747 748 749 750 751 752 753
## 3 1 2 1 5 1 10 8 6 5
## 754 755 756 757 758 759 760 761 762 763
## 5 7 2 4 6 2 3 4 4 2
## 764 765 766 767 768 769 770 771 772 773
## 4 7 3 4 2 2 7 3 7 5
## 774 775 776 777 778 779 780 781 782 783
## 3 6 5 4 2 2 3 1 3 4
## 784 785 786 787 788 789 790 791 793 795
## 5 3 1 5 1 3 2 8 2 3
## 796 797 798 799 800 801 802 803 804 805
## 2 2 1 2 7 1 2 2 8 7
## 806 807 808 809 810 811 812 813 814 815
## 3 2 2 5 5 1 1 1 7 5
## 816 817 818 819 820 821 822 823 824 825
## 2 2 3 2 4 2 5 3 2 1
## 826 827 828 829 830 831 832 833 834 835
## 1 1 1 5 4 1 4 1 4 4
## 836 837 838 839 840 841 842 843 844 845
## 2 3 3 3 5 3 7 1 2 7
## 846 847 848 849 850 851 852 853 854 855
## 4 1 3 3 6 4 2 3 2 7
## 856 857 858 859 860 861 862 863 864 865
## 3 2 2 3 1 5 6 1 6 3
## 866 867 868 869 870 872 873 874 875 876
## 2 1 2 4 6 4 3 3 5 5
## 877 878 879 880 881 882 883 884 885 886
## 2 1 3 5 2 3 3 4 3 5
## 887 888 889 890 891 892 893 894 895 896
## 8 2 1 6 3 2 4 2 6 3
## 897 898 899 900 902 903 904 905 906 907
## 3 5 1 4 4 2 3 4 2 2
## 908 909 910 912 913 914 915 916 917 918
## 1 2 1 5 2 1 2 2 7 4
## 919 920 921 922 923 924 925 926 927 928
## 3 1 2 3 2 3 2 3 4 3
## 929 930 931 932 933 934 935 936 937 938
## 1 2 7 6 2 5 1 5 2 4
## 939 940 941 942 943 944 945 946 947 948
## 2 2 3 2 2 1 2 4 3 2
## 949 951 952 953 954 955 957 959 960 961
## 4 3 3 1 2 2 2 5 5 2
## 962 963 965 966 969 970 971 972 973 974
## 2 1 1 1 4 1 4 3 1 1
## 975 976 977 978 979 980 982 983 984 985
## 2 7 3 2 1 3 2 2 2 3
## 986 987 988 989 990 991 992 993 994 995
## 1 1 2 2 1 1 5 2 4 4
## 996 997 998 999 1000 1001 1002 1003 1004 1005
## 4 3 5 1 2 4 4 5 4 2
## 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015
## 3 1 3 2 6 7 3 3 3 1
## 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025
## 4 2 4 1 1 3 1 3 4 2
## 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035
## 6 2 3 3 1 2 3 1 3 3
## 1037 1038 1039 1040 1042 1043 1044 1046 1047 1048
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## 16546 16547 16563 16567 16574 16584 16586 16592 16594 16610
## 1 1 1 1 1 1 1 1 1 1
## 16614 16668 16688 16748 16751 16757 16761 16792 16808 16813
## 1 2 1 1 1 1 1 1 1 1
## 16821 16826 16828 16836 16855 16866 16868 16882 16885 16933
## 1 1 1 1 1 1 1 3 1 1
## 16942 16953 16970 16975 17000 17002 17009 17012 17032 17042
## 1 1 1 1 1 1 1 1 1 1
## 17044 17051 17056 17070 17083 17084 17092 17097 17103 17117
## 1 1 1 1 1 1 1 1 1 1
## 17126 17133 17139 17148 17165 17167 17175 17186 17188 17191
## 1 1 1 1 1 1 1 1 1 1
## 17197 17201 17203 17209 17219 17234 17252 17261 17273 17290
## 1 1 1 1 1 1 1 1 1 2
## 17316 17354 17368 17377 17396 17404 17408 17420 17422 17430
## 1 1 1 1 2 1 1 1 1 1
## 17444 17459 17460 17462 17477 17489 17496 17529 17530 17533
## 1 1 1 1 1 1 1 1 1 1
## 17546 17547 17560 17588 17590 17591 17594 17597 17607 17643
## 1 1 1 1 1 1 1 1 1 1
## 17644 17649 17667 17689 17707 17715 17724 17727 17731 17741
## 1 1 1 1 1 1 1 1 1 1
## 17761 17774 17792 17829 17833 17860 17868 17871 17872 17891
## 2 1 1 1 1 1 1 1 1 1
## 17895 17909 17911 17920 17943 17984 17989 17998 18037 18067
## 2 1 1 1 1 1 1 1 1 1
## 18077 18079 18084 18093 18095 18103 18134 18136 18138 18156
## 1 1 1 1 1 1 1 1 1 1
## 18170 18201 18205 18210 18214 18226 18239 18254 18265 18274
## 1 1 1 1 1 1 1 1 1 1
## 18288 18302 18312 18319 18324 18325 18330 18340 18344 18352
## 1 1 1 1 1 1 1 1 2 1
## 18355 18359 18364 18375 18376 18377 18403 18406 18432 18447
## 1 1 1 1 1 1 1 1 1 1
## 18454 18458 18475 18480 18499 18509 18532 18534 18536 18537
## 1 1 1 1 1 1 1 1 1 1
## 18547 18576 18580 18581 18584 18628 18632 18652 18667 18671
## 1 1 1 1 1 3 1 1 1 1
## 18674 18678 18686 18698 18718 18720 18723 18729 18737 18747
## 5 2 1 1 1 1 1 1 1 1
## 18822 18839 18854 18859 18861 18866 18893 18908 18929 18930
## 1 1 1 1 1 1 1 1 1 2
## 18932 18971 18978 18983 18986 18992 18998 19014 19018 19038
## 1 1 2 1 1 1 1 1 1 1
## 19053 19063 19090 19100 19104 19108 19135 19145 19156 19163
## 1 1 1 1 1 1 1 1 1 1
## 19165 19172 19193 19212 19226 19260 19263 19268 19277 19302
## 1 1 2 1 1 3 1 1 1 2
## 19315 19321 19328 19341 19349 19369 19401 19403 19435 19453
## 1 2 1 1 1 1 1 1 1 1
## 19458 19460 19474 19498 19501 19541 19584 19589 19608 19612
## 1 1 1 1 1 1 1 1 1 1
## 19638 19641 19659 19664 19681 19685 19688 19690 19695 19704
## 1 1 1 2 1 1 1 1 1 1
## 19707 19710 19722 19725 19726 19738 19754 19756 19772 19773
## 1 1 2 1 1 1 1 1 1 1
## 19779 19796 19849 19861 19869 19890 19911 19923 19963 20012
## 1 1 1 1 1 1 1 1 1 1
## 20058 20067 20095 20100 20107 20112 20118 20128 20135 20149
## 1 1 1 1 1 1 1 1 1 1
## 20150 20164 20172 20185 20207 20210 20218 20235 20241 20285
## 1 1 1 1 1 1 1 1 1 1
## 20286 20328 20348 20349 20373 20469 20472 20503 20510 20533
## 1 1 1 1 1 1 1 1 1 2
## 20542 20589 20604 20641 20647 20657 20664 20674 20681 20700
## 1 1 1 1 2 1 1 1 1 1
## 20729 20730 20763 20779 20785 20811 20851 20869 20874 20886
## 1 1 1 1 1 1 1 1 1 1
## 20907 20911 20928 20944 20965 20979 20990 21009 21018 21019
## 1 1 1 1 1 1 2 1 1 1
## 21026 21042 21060 21126 21135 21139 21147 21149 21157 21166
## 1 1 1 1 3 1 1 1 3 1
## 21195 21216 21251 21266 21276 21285 21297 21299 21323 21350
## 1 1 1 1 1 1 1 1 1 1
## 21369 21393 21400 21404 21446 21460 21465 21500 21505 21541
## 1 2 1 1 1 1 1 1 1 1
## 21567 21615 21618 21628 21636 21659 21691 21723 21751 21758
## 1 1 1 1 1 1 1 1 1 1
## 21783 21844 21858 21891 21893 21904 21905 21909 21928 21944
## 1 1 1 1 1 1 1 1 1 1
## 21969 21972 21980 21989 22010 22049 22058 22091 22093 22115
## 1 1 1 1 1 1 1 1 1 1
## 22144 22155 22165 22169 22174 22177 22187 22221 22228 22245
## 1 1 1 1 1 1 1 1 1 1
## 22264 22271 22273 22284 22291 22307 22332 22397 22431 22435
## 1 1 1 2 1 1 1 1 1 1
## 22449 22495 22502 22526 22529 22555 22578 22624 22668 22674
## 1 1 1 1 1 1 1 1 1 1
## 22682 22697 22713 22754 22757 22775 22776 22793 22831 22855
## 1 2 1 1 1 1 1 1 1 2
## 22871 22882 22889 22903 22922 22925 22929 22947 22963 22969
## 1 1 1 1 1 1 1 1 1 1
## 22994 23029 23034 23044 23057 23064 23066 23096 23100 23102
## 1 1 1 2 1 1 1 4 3 1
## 23107 23109 23129 23189 23210 23251 23254 23262 23302 23308
## 1 1 1 1 1 1 1 1 1 1
## 23320 23368 23415 23423 23472 23473 23476 23505 23511 23535
## 1 1 1 1 1 1 1 1 2 1
## 23549 23552 23562 23571 23601 23610 23626 23630 23644 23650
## 1 1 1 1 1 1 3 1 1 1
## 23660 23668 23671 23676 23727 23740 23748 23752 23754 23756
## 2 1 1 1 1 1 1 1 1 2
## 23759 23772 23802 23835 23867 23880 23931 23960 23973 23983
## 1 1 1 1 1 1 1 1 1 1
## 23984 24008 24012 24024 24026 24046 24050 24070 24072 24089
## 1 1 1 1 1 1 1 1 1 1
## 24096 24099 24115 24132 24150 24173 24177 24184 24199 24237
## 1 1 2 1 1 1 1 1 1 1
## 24251 24270 24280 24291 24297 24350 24351 24364 24400 24413
## 1 2 1 1 1 1 2 1 1 1
## 24442 24444 24476 24512 24589 24592 24614 24632 24642 24665
## 1 1 2 1 1 1 1 1 1 1
## 24675 24677 24701 24762 24763 24802 24808 24831 24850 24858
## 1 1 1 1 1 2 1 1 1 1
## 24865 24871 24910 24940 24975 24981 24998 25000 25018 25045
## 1 1 1 1 1 1 1 1 1 1
## 25054 25067 25108 25119 25133 25153 25166 25170 25218 25224
## 1 1 1 1 1 1 1 1 1 1
## 25255 25257 25270 25274 25280 25307 25320 25360 25389 25392
## 1 1 1 1 1 1 1 1 2 1
## 25464 25476 25500 25512 25579 25589 25611 25623 25627 25645
## 1 1 1 1 1 1 1 1 1 1
## 25651 25662 25664 25730 25735 25766 25781 25784 25911 25928
## 1 1 1 1 1 2 1 1 1 1
## 25980 26017 26043 26057 26070 26085 26098 26107 26124 26172
## 1 1 1 1 1 1 1 1 1 1
## 26175 26231 26331 26403 26412 26436 26450 26487 26536 26593
## 2 1 1 1 1 1 1 1 1 1
## 26600 26601 26622 26623 26673 26679 26704 26752 26795 26811
## 1 1 1 1 2 1 1 1 1 1
## 26813 26815 26818 26836 26838 26843 26931 26955 26978 26987
## 1 1 1 1 1 1 1 1 1 1
## 26989 27011 27021 27031 27060 27065 27075 27090 27098 27106
## 1 1 1 1 1 1 1 1 1 1
## 27129 27136 27150 27198 27311 27367 27400 27404 27460 27466
## 2 1 1 1 1 1 1 1 1 2
## 27491 27528 27551 27558 27649 27651 27663 27719 27755 27784
## 1 1 1 1 1 1 1 1 1 1
## 27787 27870 27883 27898 27927 27969 27997 28014 28034 28057
## 1 1 1 1 1 1 1 1 1 1
## 28065 28070 28094 28114 28125 28133 28147 28172 28174 28175
## 1 1 1 1 1 1 1 1 1 1
## 28200 28247 28255 28260 28277 28389 28410 28433 28463 28464
## 1 2 1 1 1 1 1 1 1 1
## 28473 28502 28504 28505 28587 28591 28600 28649 28667 28681
## 1 1 1 1 1 2 1 1 1 1
## 28684 28740 28782 28840 28929 28963 29072 29074 29082 29119
## 1 1 1 1 1 1 2 1 1 1
## 29140 29156 29183 29207 29246 29285 29319 29335 29369 29375
## 1 1 1 1 1 1 1 1 1 1
## 29403 29429 29446 29448 29487 29489 29537 29687 29688 29719
## 1 1 1 1 1 1 1 1 1 1
## 29776 29795 29809 29875 29876 29882 29997 30023 30027 30097
## 1 2 1 1 1 1 1 1 1 1
## 30112 30119 30202 30231 30239 30347 30402 30408 30417 30441
## 1 1 1 1 1 1 1 1 1 1
## 30453 30500 30520 30563 30579 30588 30645 30664 30667 30682
## 1 1 1 1 1 1 1 1 1 1
## 30691 30747 30777 30803 30920 30928 30948 30970 30997 30998
## 1 1 1 1 1 1 1 1 1 1
## 31013 31031 31035 31041 31099 31115 31176 31251 31297 31348
## 1 1 1 1 1 1 1 1 1 1
## 31352 31392 31404 31497 31533 31541 31550 31605 31622 31631
## 1 1 1 1 1 1 1 1 1 1
## 31761 31847 31894 31913 31919 32005 32006 32069 32110 32119
## 1 1 1 1 1 1 1 1 1 1
## 32138 32175 32200 32254 32326 32390 32396 32413 32497 32500
## 1 1 1 1 1 1 1 1 1 1
## 32576 32645 32683 32698 32755 32766 32790 32859 32946 32961
## 1 1 1 1 1 1 1 1 1 1
## 32969 33036 33057 33134 33135 33154 33240 33323 33324 33337
## 3 1 1 1 1 2 1 1 1 1
## 33376 33432 33463 33506 33509 33520 33555 33566 33628 33646
## 1 1 1 1 1 1 1 1 1 1
## 33773 33783 33801 33803 33835 33852 33863 33888 33925 33929
## 1 1 1 1 1 1 1 1 1 1
## 33998 34133 34171 34183 34193 34225 34336 34381 34388 34416
## 1 1 1 1 1 1 1 1 1 1
## 34434 34435 34525 34555 34645 34666 34794 34836 34874 34876
## 1 1 1 1 1 1 1 1 2 1
## 34880 34899 34911 34968 34977 34988 34990 34997 35008 35055
## 1 2 1 1 1 1 1 1 1 1
## 35096 35097 35119 35128 35169 35185 35212 35227 35250 35299
## 1 1 1 1 1 1 1 1 1 1
## 35334 35374 35454 35457 35459 35471 35514 35574 35727 35794
## 1 1 1 1 1 1 1 1 3 1
## 35849 35901 35927 35972 36153 36302 36363 36384 36471 36477
## 2 1 1 1 1 1 1 1 1 1
## 36492 36514 36598 36626 36863 36961 37003 37077 37212 37287
## 1 1 1 1 1 1 1 1 1 1
## 37291 37316 37317 37329 37339 37454 37463 37534 37642 37643
## 1 1 1 1 1 2 1 1 1 1
## 37655 37837 37855 37919 37936 37998 38068 38108 38149 38160
## 1 1 1 1 1 1 1 1 1 1
## 38212 38286 38304 38336 38365 38417 38432 38475 38489 38657
## 1 1 1 1 1 1 1 1 1 1
## 38660 38664 38665 38709 38870 38960 38996 39011 39028 39210
## 3 1 1 1 1 1 1 1 1 1
## 39227 39295 39379 39409 39470 39473 39484 39632 39856 39986
## 1 1 1 1 1 1 1 1 1 1
## 40013 40087 40189 40335 40389 40392 40482 40485 40527 40553
## 1 2 1 1 1 1 1 1 1 1
## 40633 40779 40836 40938 41014 41020 41214 41244 41361 41374
## 1 2 1 1 1 4 1 1 1 1
## 41378 41386 41661 41694 41763 41822 41975 42205 42342 42370
## 1 1 1 1 1 1 1 1 1 1
## 42387 42485 42488 42556 42824 42854 42881 42962 43064 43079
## 1 1 1 1 1 1 1 1 1 1
## 43093 43121 43200 43322 43363 43367 43437 43607 43642 43722
## 1 1 1 1 1 1 1 1 1 1
## 43761 43776 43789 43958 44036 44203 44262 44307 44369 44493
## 1 1 1 1 1 1 1 1 1 1
## 44734 44744 44859 44879 45059 45201 45202 45298 45364 45655
## 1 1 1 1 1 1 1 1 1 1
## 45726 45857 45864 45979 46010 46065 46099 46127 46216 46255
## 1 1 1 1 1 1 1 1 2 1
## 46331 46359 46394 46642 46943 46989 47008 47371 47625 47746
## 1 1 1 1 1 1 1 1 1 1
## 47766 47918 47963 47965 48009 48024 48100 48121 48150 48201
## 1 1 1 1 1 1 1 1 2 1
## 48289 48423 48487 48673 48703 48865 48992 49047 49116 49178
## 1 1 1 2 1 1 1 1 1 1
## 49229 49248 49274 49283 49454 49466 49759 49809 49818 49868
## 1 1 1 1 1 1 1 1 1 1
## 49924 50017 50163 50261 50385 50396 50421 50610 50688 50852
## 1 1 1 1 1 1 1 1 1 1
## 51103 51119 51252 51344 51370 51788 51847 52033 52047 52379
## 1 1 1 1 1 1 1 1 1 1
## 52456 52480 52612 52820 52844 53054 53083 53148 53215 53335
## 1 1 1 1 1 1 1 1 1 1
## 53351 53420 53439 53442 53622 53798 53824 54000 54007 54068
## 1 1 1 1 1 1 1 1 1 1
## 54364 54480 54550 54596 54782 54881 54915 54918 55111 55462
## 1 1 1 1 1 1 1 1 1 1
## 55716 55869 55958 56254 56288 56502 56716 56743 57252 57265
## 1 1 1 1 1 1 1 1 1 1
## 57376 57580 57884 57979 58221 58365 58463 58521 58565 58583
## 1 1 1 1 1 1 1 1 1 1
## 58678 58708 58858 59241 59415 59613 59692 59860 59883 60170
## 1 1 1 1 1 1 2 1 1 1
## 60308 60310 60346 60433 60510 60571 60616 60966 60997 61085
## 1 1 1 1 1 1 1 1 1 1
## 61231 61350 61393 61442 61564 61635 61745 61821 61981 62092
## 1 1 1 1 1 1 1 1 1 1
## 62129 62259 62312 62348 62512 62891 62903 63047 63217 63290
## 1 1 1 1 1 1 1 1 1 1
## 63373 63482 63558 63743 63897 64116 64420 64519 64538 64587
## 1 1 1 2 1 1 1 1 1 1
## 64595 64839 64868 65216 65320 65938 65951 65959 66422 66466
## 1 1 1 1 1 1 1 1 1 1
## 66600 66852 67434 67449 68013 68123 68304 68587 68828 68900
## 1 1 1 1 1 2 1 1 1 1
## 69276 69313 69483 69551 69823 69875 69907 70000 70132 70146
## 1 1 1 1 1 1 1 1 1 1
## 70334 70456 70567 70659 70734 70983 71328 72051 72112 72113
## 1 1 1 5 1 1 1 1 1 1
## 72121 72156 72302 72313 72705 72817 72997 73118 73323 73490
## 1 1 1 1 1 1 1 1 1 1
## 73661 73936 74579 74844 74990 75492 76008 76588 76840 77300
## 1 2 2 1 1 1 1 1 1 1
## 77384 77422 77771 77853 77985 78097 78380 78750 78935 79522
## 1 1 1 1 1 1 1 1 1 1
## 79574 80097 80346 80441 80646 80792 80975 81004 81495 81723
## 1 1 1 1 1 1 1 1 1 1
## 82271 82580 82708 82980 83138 83534 83756 83956 84427 84691
## 1 1 1 1 1 1 1 1 1 1
## 84834 84933 85065 85803 85885 85953 86101 86127 86282 86303
## 1 1 1 1 1 1 1 1 1 1
## 86351 86566 86730 87588 89000 89265 89523 89827 90536 90588
## 2 1 1 1 1 1 1 1 1 1
## 90756 91162 91501 91554 91636 91687 92177 92467 92753 93237
## 1 1 1 1 1 1 2 1 1 1
## 93593 95043 95280 95320 95389 95441 97020 97773 99792 99979
## 1 1 1 1 1 1 1 1 1 1
## 99991 101212 101497 101512 101644 102546 102936 102959 103076 103505
## 2 1 1 1 1 1 1 2 1 1
## 103709 103884 103975 104768 105340 105575 106071 106156 107319 107354
## 1 1 1 1 1 1 2 1 1 1
## 108415 109820 109956 110541 111524 111690 111873 112221 112684 113205
## 1 1 1 1 1 1 1 1 1 1
## 113552 114385 114872 116014 116896 117937 119147 119660 120153 120642
## 1 1 1 1 1 1 1 1 1 1
## 121379 122690 122868 123828 123871 124318 124471 124651 124691 124858
## 1 1 1 1 1 1 1 2 1 1
## 124888 126638 126830 127058 127472 127850 128639 128864 128993 129746
## 1 1 1 1 1 1 2 1 1 1
## 130093 131214 134322 135229 136476 142263 143329 144886 145618 149901
## 1 1 1 3 1 1 1 1 2 1
## 153237 155578 157422 158486 160039 161344 161475 161782 164607 165097
## 1 1 1 1 1 1 1 1 1 1
## 168648 171093 172240 173334 174862 175281 176347 179158 183396 188818
## 1 1 1 1 1 1 1 1 1 1
## 190585 192016 202741 205400 215315 223738 225595 230291 241707 242333
## 1 1 1 1 1 1 1 1 1 1
## 249209 255963 265084 279970 284169 327677 444745 463881
## 1 1 1 1 1 1 1 1ggplot(data = DelinquenciesValues, aes(x = AmountDelinquent))+
geom_histogram(binwidth = 10)+
coord_cartesian(xlim = c(0,2000))+
ggtitle('Count of Loans by Amount Delinquent')
The data above in the histograms and table shows that the majority of Prosper borrowers have 0 dollars in delinquency, a good sign if you are a lender. After adjusting the histogram to account for this reality (removing all values with 0), we see that Prosper, as expected,
Borrower Data Exploration: Subsection: Delinquencies Last 7 Years
Examining the Delinquencies Last 7 Years variable will help us understand the type of borrowers that are included in this dataset. DelinquenciesLast7Years may provide a glimpse into the reliability of borrowers in this set.
sort(table(loans$DelinquenciesLast7Years), decreasing = T)##
## 0 1 3 2 4 5 6 7 8 9 10 11
## 76439 3967 3183 2879 2592 1826 1790 1648 1421 1208 1151 1075
## 12 13 14 15 16 17 18 20 19 21 23 24
## 982 873 821 795 731 608 574 565 540 472 439 423
## 22 25 26 27 28 29 30 32 31 35 33 34
## 421 347 330 317 296 287 248 225 214 201 190 190
## 37 39 36 38 42 40 44 99 41 43 47 46
## 153 148 147 144 128 113 110 110 106 101 94 90
## 45 48 49 50 51 52 56 60 53 54 55 62
## 81 78 74 72 72 55 53 41 40 40 39 36
## 59 61 65 58 63 57 64 66 67 75 68 69
## 34 34 34 31 31 30 28 27 22 22 20 20
## 73 70 77 72 71 80 82 76 78 74 88 79
## 17 15 15 14 13 12 12 10 10 9 9 8
## 84 86 87 90 83 92 89 81 91 95 96 97
## 8 7 7 7 6 6 5 4 4 4 4 4
## 85 94 98 93
## 3 3 3 2summary(loans$DelinquenciesLast7Years)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.000 0.000 0.000 4.155 3.000 99.000 990Findings : Unsurprisingly, we see the vast majority of delinquent loans in the last 7 years for borrowers at 0. The median reflects this by also being 0, however, a mean of 4.155 shows that there are some potentially large amounts of delinquencies in the last 7 years per borrowers that may be driving this value up. In the table, we see that there are, in fact, 110 borrowers who have 99 delinquencies in the past 7 years. This appears to be a strange lift from 98 (3 total borrowers). Is this a maximum value? Could it be human error?
qplot(data = loans ,x=DelinquenciesLast7Years, binwidth = 1)+
geom_histogram()+
scale_x_continuous()+
scale_y_continuous(
limits = c(0,100000)
)+
ggtitle('Count of Delinquencies Last 7 Years')## Warning: Removed 990 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 990 rows containing non-finite values (stat_bin).
Findings: A simple histogram shows that, in fact, the majority of delinquencies in last 7 years for borrowers were negatively skewed, unsurprisingly considering that banks and lenders are in the business of ensuring their loans are paid back. Let’s examine and plot that surreptitious the DelinquenciesLast7Years on the larger end of the plot.
qplot(data = loans, x = loans$DelinquenciesLast7Years)+
geom_histogram(binwidth = 1)+
scale_x_continuous(
limits = c(80,100)
)+
ggtitle('Count of Delinquencies Last 7 years')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 113717 rows containing non-finite values (stat_bin).
## Warning: Removed 113717 rows containing non-finite values (stat_bin).
> Findings The histogram from DelinquenciesLast7Years > 79 show that the #99 is a strange occurance that may be artifically driving the mean up for the total DelinquenciesLast7Years. We will attempt to determine, later in this analysis, what makes an individual become delinquent with some multivariate tests and plots.
Borrower Data Exploration: Subsection: BorrowerAPR We are getting a better sense of the types of borrowers Prosper loans money to. Now, we will examine the BorrowerAPR to determine how Prosper makes $ of their customers.
qplot(data = loans ,x=BorrowerAPR)+
geom_histogram(binwidth = .01)+
ggtitle('Count of Loans by Borrower APR')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 25 rows containing non-finite values (stat_bin).
## Warning: Removed 25 rows containing non-finite values (stat_bin).
The findings above dictate a few peaks: Once between .15 and .20, again at .3, and once more at around .36. Let’s create a sorted table to examine these trends.
head(sort(table(loans$BorrowerAPR), decreasing = T), 20)##
## 0.35797 0.35643 0.37453 0.30532 0.2951 0.35356 0.29776 0.15833 0.24246
## 3672 1644 1260 902 747 721 707 652 605
## 0.24758 0.12528 0.17359 0.15324 0.27462 0.27285 0.13799 0.15713 0.12691
## 601 559 549 547 534 506 489 482 456
## 0.25781 0.20735
## 444 433summary(loans$BorrowerAPR)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.00653 0.15629 0.20976 0.21883 0.28381 0.51229 25Interestingly, we see that Prosper’s most commonly issued APR is .3672, this is well above the mean of .21976 and the median of .20976.
Let’s remove all NA’s from APR for analysis - adding the Mean line, we can examine how many values are falling above or below the mean.
Clean_APR <- subset(loans, !is.na(BorrowerAPR))
mean(Clean_APR$BorrowerAPR)## [1] 0.2188277qplot(data = Clean_APR ,x=BorrowerAPR, binwidth = .01)+
geom_histogram()+
scale_x_continuous(breaks = seq(0,0.4,.02))+
geom_vline(xintercept = mean(Clean_APR$BorrowerAPR), color = 'green', linetype = 'longdash')+
ggtitle('Count of Loans by Borrower APR')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
We see a number of peaks and valleys within the BorrowerAPR data, which suggests there are certain integers that Prosper commonly issues when it comes to BorrowerAPR.
Borrower Data Exploration: Subsection: Income Range
summary(loans$IncomeRange)## $0 $1-24,999 $100,000+ $25,000-49,999 $50,000-74,999
## 621 7274 17337 32192 31050
## $75,000-99,999 Not displayed Not employed
## 16916 7741 806loans_IncomeRanges <- subset(loans, loans$IncomeRange != "Not displayed")
summary(loans_IncomeRanges$IncomeRange)## $0 $1-24,999 $100,000+ $25,000-49,999 $50,000-74,999
## 621 7274 17337 32192 31050
## $75,000-99,999 Not displayed Not employed
## 16916 0 806qplot(data=loans_IncomeRanges, x=loans_IncomeRanges$IncomeRange)+
geom_bar()+
ggtitle('Count of Loans by Income Range')
Findings
qplot(data=loans, x=BorrowerState)+
geom_bar()+
ggtitle('Count of Loans by Borrower State')
sort(table(loans$BorrowerState), decreasing = T)##
## CA TX NY FL IL GA OH MI VA NJ NC
## 14717 6842 6729 6720 5921 5515 5008 4197 3593 3278 3097 3084
## WA PA MD MO MN MA CO IN AZ WI OR TN
## 3048 2972 2821 2615 2318 2242 2210 2078 1901 1842 1817 1737
## AL CT SC NV KS KY OK LA UT AR MS NE
## 1679 1627 1122 1090 1062 983 971 954 877 855 787 674
## ID NH NM RI HI WV DC MT DE VT AK SD
## 599 551 472 435 409 391 382 330 300 207 200 189
## IA WY ME ND
## 186 150 101 52California has the largeset amount of users on Prosper with 14,717 borrowers, while North Dakota has the least with 52 borrowers.
Borrower Subsection: TotalInquiries
qplot(data=loans, x=TotalInquiries)+
geom_histogram()+
ggtitle('Count of Loans by Total Inquiries')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 1159 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 1159 rows containing non-finite values (stat_bin).
head(sort(table(loans$TotalInquiries), decreasing = T), 20)##
## 2 3 1 4 5 0 6 7 8 9 10 11
## 14887 13934 13785 12148 10098 8430 7607 6171 4692 3779 2914 2431
## 12 13 14 15 16 17 18 19
## 1786 1453 1245 978 864 724 581 539The data above show that most borrowers have very few inquiries on their credit, potentially showing that Prosper selects those who are steadfast and committed to paying down their debts.
qplot(data=loans, x=DebtToIncomeRatio)+
geom_histogram()+
ggtitle('Count of Loans by Debt To Income Ratio')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 8554 rows containing non-finite values (stat_bin).## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 8554 rows containing non-finite values (stat_bin).
Given that the 10 value appears to be an anomaly, let’s run a summary on Debt to Income Ratio
summary(loans$DebtToIncomeRatio)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 0.000 0.140 0.220 0.276 0.320 10.010 8554Let’s further examine Debt to Income Ratios that are above the 3rd Quartile
High_DTIR <- subset(loans, loans$DebtToIncomeRatio > .32)
sort(table(High_DTIR$DebtToIncomeRatio),decreasing = T)##
## 0.33 0.35 0.34 0.36 0.37 0.38 0.39 0.4 0.41
## 1902 1812 1810 1523 1399 1364 1226 1109 995
## 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.5
## 893 851 753 697 634 617 524 470 447
## 0.51 0.52 0.54 0.53 0.55 10.01 0.56 0.57 0.59
## 431 372 341 320 279 272 244 229 182
## 0.58 0.6 0.61 0.62 0.63 0.65 0.64 0.66 0.67
## 166 149 140 120 108 105 91 78 77
## 0.68 0.71 0.7 0.69 0.72 0.75 0.73 0.76 0.74
## 72 67 64 58 58 51 43 43 40
## 0.78 0.77 0.86 0.87 0.81 0.84 0.85 0.79 0.83
## 38 35 29 29 27 27 27 26 26
## 0.8 0.82 0.88 0.89 0.9 0.91 0.94 0.96 0.97
## 24 22 22 22 20 19 19 19 18
## 0.92 0.93 1 0.98 0.99 1.02 0.95 1.01 1.05
## 15 14 14 13 13 12 11 11 11
## 1.06 1.07 1.03 1.19 1.21 1.04 1.12 1.16 1.08
## 11 11 10 10 10 8 8 8 7
## 1.1 1.27 1.14 1.15 1.18 1.22 1.49 1.2 1.25
## 7 7 6 6 6 6 6 5 5
## 1.31 1.56 1.09 1.11 1.24 1.32 1.36 1.47 1.54
## 5 5 4 4 4 4 4 4 4
## 2.2 1.13 1.29 1.34 1.39 1.41 1.42 1.45 1.46
## 4 3 3 3 3 3 3 3 3
## 1.6 1.75 1.79 1.81 1.87 1.89 1.99 2.3 2.38
## 3 3 3 3 3 3 3 3 3
## 2.45 2.72 3.49 3.92 1.17 1.23 1.26 1.28 1.3
## 3 3 3 3 2 2 2 2 2
## 1.37 1.38 1.5 1.51 1.52 1.55 1.57 1.58 1.61
## 2 2 2 2 2 2 2 2 2
## 1.65 1.72 1.74 1.8 1.82 1.93 1.94 1.98 2.02
## 2 2 2 2 2 2 2 2 2
## 2.07 2.1 2.19 2.34 2.5 2.6 2.65 2.79 2.95
## 2 2 2 2 2 2 2 2 2
## 2.99 3.23 3.27 3.53 3.64 3.73 3.81 4.4 4.43
## 2 2 2 2 2 2 2 2 2
## 4.71 4.9 5.36 5.56 7.27 0.32007 0.321 0.32388 0.33348
## 2 2 2 2 2 1 1 1 1
## 0.34443 0.34452 0.35155 0.35333 0.3543 0.3555 0.35972 0.36006 0.36232
## 1 1 1 1 1 1 1 1 1
## 0.36331 0.37002 0.37772 0.38361 0.3838 0.38587 0.39181 0.39531 0.39846
## 1 1 1 1 1 1 1 1 1
## 0.40466 0.40475 0.40572 0.4137 0.41586 0.42965 0.42972 0.43886 0.4413
## 1 1 1 1 1 1 1 1 1
## 0.46403 0.499 0.50136 0.50872 0.51504 0.54433 0.56576 0.57091 0.60618
## 1 1 1 1 1 1 1 1 1
## 0.78342 1.35 1.4 1.43 1.44 1.53 1.59 1.62 1.64
## 1 1 1 1 1 1 1 1 1
## 1.66 1.67 1.68 1.69 1.7 1.73 1.76 1.78 1.85
## 1 1 1 1 1 1 1 1 1
## 1.86 1.9 1.92 1.95 1.96 2.05 2.08 2.09 2.11
## 1 1 1 1 1 1 1 1 1
## 2.14 2.16 2.18 2.21 2.22 2.23 2.25 2.27329 2.28
## 1 1 1 1 1 1 1 1 1
## 2.31 2.35 2.43 2.47 2.48 2.49 2.53 2.55 2.57
## 1 1 1 1 1 1 1 1 1
## 2.59 2.63 2.66 2.67 2.7 2.74 2.83 2.86 2.94
## 1 1 1 1 1 1 1 1 1
## 2.97 3.07 3.09 3.11 3.14 3.17 3.19 3.22 3.26
## 1 1 1 1 1 1 1 1 1
## 3.28 3.29 3.32 3.38 3.39 3.45 3.54 3.58 3.59
## 1 1 1 1 1 1 1 1 1
## 3.66 3.68 3.71 3.76 3.77 3.86 4 4.03 4.04
## 1 1 1 1 1 1 1 1 1
## 4.13 4.14 4.15 4.16 4.19 4.21 4.27 4.29 4.32
## 1 1 1 1 1 1 1 1 1
## 4.33 4.37 4.42 4.44 4.54 4.58 4.66 4.68 4.75
## 1 1 1 1 1 1 1 1 1
## 4.76 4.78 4.84 4.85 4.86 4.89 5.02 5.05 5.06
## 1 1 1 1 1 1 1 1 1
## 5.1 5.15 5.16 5.18 5.21 5.23 5.26 5.29 5.31
## 1 1 1 1 1 1 1 1 1
## 5.34 5.38 5.55 5.5608 5.59 5.64 5.65 5.67 5.69
## 1 1 1 1 1 1 1 1 1
## 5.76 5.98 6.01 6.05 6.06 6.07 6.2 6.37 6.49
## 1 1 1 1 1 1 1 1 1
## 6.51 6.66 6.68 6.85 6.95 6.96 7.06 7.22 7.42
## 1 1 1 1 1 1 1 1 1
## 7.47 7.52 7.59 7.79 7.9 7.99 8.06 8.13 8.27
## 1 1 1 1 1 1 1 1 1
## 8.52 8.53 8.63 9.06 9.2 9.44 9.77
## 1 1 1 1 1 1 1From the data above, that there are a few loans at various price points that have obscenely high debt to income ratios. Perhaps these folks have a great deal of collateral to put up.
qplot(data=loans, x=EmploymentStatus)+
geom_bar()+
ggtitle('Count of Loans by Employment Status')
The graph above shows that most borrowers are “employed” or categorized as “full-time”
qplot(data = loans, x=ProsperRating..numeric.)+
geom_bar()+
ggtitle('Count of Loans by Prosper Rating Numeric')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 29084 rows containing non-finite values (stat_bin).## Warning: Removed 29084 rows containing non-finite values (stat_count).
Let’s examine the credit scores of applicant’s by creating a new variable that takes the mean of credit score upper and credit score lower. We will, when creating a histogram, start the x-axis at 300 to avoid lower values that are outliers or have omitted values.
loans$AvgCreditScore <- (loans$CreditScoreRangeLower + loans$CreditScoreRangeUpper) / 2ggplot(data = loans, aes(x = loans$AvgCreditScore), binwidth = 50)+
geom_histogram()+
scale_x_continuous(breaks = seq(250,850,50), limits = c(250,850))+
ggtitle('Count of Loans by Average Credit Score')## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.## Warning: Removed 963 rows containing non-finite values (stat_bin).## Warning: Removed 1 rows containing missing values (geom_bar).
From the above, we can see that most credit scores fall within 650 and 700. Let’s bucket those credit scores to create a categorical variable for later analysis.
loans$csBucket <- cut(loans$AvgCreditScore, breaks = c(400, 500, 600, 700, 800, 900))
ggplot(data = subset(loans, !is.na(csBucket)), aes(x=csBucket))+
geom_bar()+
ggtitle('Count of Loans by Credit Score Bucket')
When we look at the bucket bar chart below, we see there are a nearly equal amount of loans provided to average credit scores of between 600-700 and 700-800, with very few happening below or above.
Univariate Analysis
Tip: Now that you’ve completed your univariate explorations, it’s time to reflect on and summarize what you’ve found. Use the questions below to help you gather your observations and add your own if you have other thoughts!
What is the structure of your dataset?
The structure of the dataset includes 113,937 observations of 81 variables, meaning there are 113,937 individual loans oberved. We have created two new variables to better examine credit score. avgCreditScore takes the average of the upper and lower credit score to take the mean for each individual borrower. The new variable CSBucket is a categorical variable that will help determine how credit may influence loans.
What is/are the main feature(s) of interest in your dataset?
The main features of interest for me in the dataset include: Prosper Score: What factors contribute most, or have the highest correlation, to establshing a Prosper rating.
Also, is the LoanOriginalAmount for highly related to Income Range and credit score?
What other features in the dataset do you think will help support your
investigation into your feature(s) of interest?
I am also interested in what levels of credit scores influence the eventual borrower APR. Are there distinct patterns between the credit worthiness of a borrower and whether they get a loan?
Did you create any new variables from existing variables in the dataset?
Yes, I created the avgCreditScore variable to determine what number lies between the lower and upper credit score for each user. Then, I used the cut() function in order to bin the average credit scores per user.
Of the features you investigated, were there any unusual distributions?
Did you perform any operations on the data to tidy, adjust, or change the form
of the data? If so, why did you do this?
I had removed na’s and blank values from a number of individual datapoints in order to better run analysis such as bar graphs.
Bivariate Plots Section
Tip: Based on what you saw in the univariate plots, what relationships between variables might be interesting to look at in this section? Don’t limit yourself to relationships between a main output feature and one of the supporting variables. Try to look at relationships between supporting variables as well.
Loan original amount by Prosper Rating
##
## 1 2 3 4 5 6 7
## 6935 9795 14274 18345 15581 14551 5372
From the box plot above, we see that loans with Prosper Ratings of A, AA, and BB have much higher quartiles, outliers, and loan original amounts, which makes sense given that Prosper Ratings of C, D, E, HR are of lesser quality according to the Prosper website.
Let’s limit the ylim to further examine the median of the loan categories.
qplot(data = loans, y=loans$LoanOriginalAmount, x = loans$ProsperRating..Alpha.,
geom='boxplot')+
coord_cartesian(ylim = c(0,20000))+
ggtitle('Loan Original Amount by Prosper Rating Alpha')
From the zoomed in data, we can see that AA loans have the highest median of any categoryat slightly above 10,000. Let’s run a table to see what the median # actually is.
by(loans$LoanOriginalAmount, loans$ProsperRating..Alpha., summary)## loans$ProsperRating..Alpha.:
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 2500 4500 6159 7904 25000
## --------------------------------------------------------
## loans$ProsperRating..Alpha.: A
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 5850 10000 11460 15000 35000
## --------------------------------------------------------
## loans$ProsperRating..Alpha.: AA
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 6000 10940 11584 16000 35000
## --------------------------------------------------------
## loans$ProsperRating..Alpha.: B
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 6000 10000 11622 15000 35000
## --------------------------------------------------------
## loans$ProsperRating..Alpha.: C
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 5000 10000 10392 15000 25000
## --------------------------------------------------------
## loans$ProsperRating..Alpha.: D
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 4000 6100 7083 10000 15000
## --------------------------------------------------------
## loans$ProsperRating..Alpha.: E
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 3600 4000 4586 5000 15900
## --------------------------------------------------------
## loans$ProsperRating..Alpha.: HR
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 3000 4000 3463 4000 16800The table above shows AA ratings with the median of 10,940, the highest of any category.
**Loan original amount by Delinquencies Last 7 Years* We’ve examined the loan original amount from the Prosper Rating, let’s see if borrower delinquencies have any effect on the loan original amount.
ggplot(data = loans, aes(x =loans$DelinquenciesLast7Years, y=loans$LoanOriginalAmount))+
geom_point()+
ggtitle('Loan Original Amount by Delinquencies Last 7 years')## Warning: Removed 990 rows containing missing values (geom_point).
The plot above shows some obvious levels to the data, as Propser seems to provide loans in 5,000 increments, however, we do see a slight pattern in which, when Delinquencies in the last 7 years rise, the total amount of a loan often falls.
Let’s add transparency and jitter in order to account for overplotting.
ggplot(data = loans, aes(x =loans$DelinquenciesLast7Years, y=loans$LoanOriginalAmount))+
geom_point(alpha = 1/30, position = "jitter")+
ggtitle('Loan Original Amount by Delinquencies Last 7 years')## Warning: Removed 990 rows containing missing values (geom_point).
The above chart, with it’s dark line on the y-axis at 0, shows that Prosper very much likes to provide loans to those with little to no delinquencies in the past 7 years. There are a few points at 99 in the chart, which may be an anomoly or human error, and is worth further questioning of Prosper’s data capture.
Loan original amount by Employment Status Building on the picture we are beginning to see with regards to loan original amount, let’s examine Employment status and loan original amount.
summary(loans$EmploymentStatus)## Employed Full-time Not available Not employed
## 2255 67322 26355 5347 835
## Other Part-time Retired Self-employed
## 3806 1088 795 6134In this data, I will create a new DF called loans_by_employmentstats as there are 2255 borrowers in which the status is blank, you can see this in the table abbove.
loans_by_employment <- subset(loans, loans$EmploymentStatus != "")
qplot(data = loans_by_employment, y=loans_by_employment$LoanOriginalAmount, x = loans_by_employment$EmploymentStatus,
geom='boxplot')+
ggtitle('Loan Original Amount by Employment')
The boxplot above shows that employed Prosper borrowers, either through a company or self-employed, have higher median loan amounts than other categories, including Full-time and Part-time. This is odd, as employed persons are logically either employed full-time or part-time or self-employed. This is a question for Prosper as to what the classification methodology is.
qplot(data = loans_by_employment, y=loans_by_employment$LoanOriginalAmount, x = loans_by_employment$EmploymentStatus,
geom='boxplot')+
coord_cartesian(ylim = c(0,20000))+
geom_hline(yintercept = median(loans_by_employment$LoanOriginalAmount), color = "green")+
ggtitle('Loan Original Amount by Number of Investors and Employment Status')
By placing the overall median line on the graph, we see that only the categories of “Employed” and “self-employed” actually have a higher median amount than the overall median, with the other categories falling behind.
Loan Original Amount by Estimated Return We’ve got a sense of the borrowers, now let’s take a look at the loan itself by examining the loan original amount and its estimated return.
ggplot(data = loans, aes(x=loans$EstimatedReturn, y=loans$LoanOriginalAmount))+
geom_point(alpha = 1/20, position = 'jitter')+
ggtitle('Loan Original Amount by Estimated Return')## Warning: Removed 29084 rows containing missing values (geom_point).
The graph above, with slight transparency and jitter, show that the estimated return for most loans is falling around .05 and 1.5. Interestingly, there are a fair amount of loans that have negative returns, much more than those that have estimated returns of .2 or more.
A Pearson correlation test below shows a negative correlation of -.28. I would have predicted greater correlation, however, the negative number suggests as the loan original amount increases, the estimated return decreases, a common phenomenmon.
cor.test(loans$EstimatedReturn, loans$LoanOriginalAmount)##
## Pearson's product-moment correlation
##
## data: loans$EstimatedReturn and loans$LoanOriginalAmount
## t = -86.98, df = 84851, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## -0.2922833 -0.2799279
## sample estimates:
## cor
## -0.2861175Loan original amount by Investors
mean(loans$Investors)## [1] 80.47523By taking the mean amount of investors per loan, which is calculated to around 80, we can begin to see how many people it actually takes to get a Prosper loan fully-funed. A scatterplot can visualize this phenomeon.
ggplot(data = loans, aes(x = loans$Investors, y = loans$LoanOriginalAmount))+
geom_point(alpha = 1/10)+
geom_vline(xintercept = mean(loans$Investors), color = "green")+
ggtitle('Loan Original Amount by Number of Investors')
The scatter plot above shows that, as loan amounts grow, so do the total amount of investors needed. The mean of just above 80 shows that the majority of loans are falling at a similar price level, thus a similar amount of investors are needed for analogous loans.
A correlation below shows a Pearson score of .38, lesser than what I expected.
cor.test(loans$Investors, loans$LoanOriginalAmount)##
## Pearson's product-moment correlation
##
## data: loans$Investors and loans$LoanOriginalAmount
## t = 138.71, df = 113940, p-value < 2.2e-16
## alternative hypothesis: true correlation is not equal to 0
## 95 percent confidence interval:
## 0.3751140 0.3850494
## sample estimates:
## cor
## 0.3800926Loan original amount by Credit Score
We will, finally, use our newly binned data to examine loan original amount by credit score bucket. This will provide a nice picture as to which credit score buckets have the highest median Loan Original amount.
qplot(data = loans, y=LoanOriginalAmount, x = csBucket,
geom='boxplot')+
geom_hline(yintercept = median(loans$LoanOriginalAmount), color = "green")+
ggtitle('Loan Original Amount by Credit Score Bucket')
Unsurprsiingly, the buckets of 700-800 and 800-900 both have medians that exceed the overall median. It is interesting to note that 600-700 credit scores have a median Loan Original Amount less than the overall median, an indication credit scores in this area are not deemed as worthy for a loan.
Bivariate Analysis
Tip: As before, summarize what you found in your bivariate explorations here. Use the questions below to guide your discussion.
Talk about some of the relationships you observed in this part of the
investigation. How did the feature(s) of interest vary with other features in
the dataset?
Most interestingly, I discovered that a credit score of 600-700 has a substantially lower median loan original amount than credit scores of 700-800. This was surprising to me, as I suspected a slight decrease but, personally, have always considered a credit score of 600-700 to be somewhat trustworthy.
Also, the total amount of investors per loan was quite intriguing, as there were substantial outliers from the mean of 80 per loan. We will further examine this by exploring categories that may influence that in the multi-variate analysis portion.
Did you observe any interesting relationships between the other features
(not the main feature(s) of interest)?
Yes, the relationship between employment status was particularly interesting, as “full time” employees have a signficiantly lower median loan amount than those simply categorized as “employed”. I suspect there may be an error in Prosper’s classification system.
What was the strongest relationship you found?
The relationship between total investors and dollar amount had a Pearson score of .38, the strongest relationship I uncovered.
Interestingly, loan original amount and estimated return were negatively correlated, showing that as a loan amount is greater, estimated returns are generally expected to fail.
Multivariate Plots Section
Tip: Now it’s time to put everything together. Based on what you found in the bivariate plots section, create a few multivariate plots to investigate more complex interactions between variables. Make sure that the plots that you create here are justified by the plots you explored in the previous section. If you plan on creating any mathematical models, this is the section where you will do that.
Examining loan original amound and borrower APR by Credit Score Bucket.
The above scatterplot shows that csBucket 800-900 are largely consolidated at a little less than .1 for their Borrower APR, despite loan amount. This shows that Prosper generally loans funds to those with good credit at various levels of dollar amount.
You can see distinct, almost vertical patterns of increased BorrowerAPR based on their credit score. Lower credit scores from 400-600 are largely consolidated lower on the y-axis at varying APRs, showing that credit scores that are lesser do not get loaned as large amounts as other credit scores.
Examining loan original amount and estimated return by Credit Score Bucket.
ggplot(data = subset(loans,!is.na(loans$csBucket)), aes(x = EstimatedReturn, y = LoanOriginalAmount))+
geom_point(aes(color = csBucket))+
ggtitle('Loan Original Amount by Estimated Return and Credit Score Bucket')## Warning: Removed 28359 rows containing missing values (geom_point).
Similarly to our analysis on borrower apr, estimated returns are largely attributed to certain credit scores. The highest end of credit scores (800-900), have a distinct Estimated Return of around .05 percent, with 700-800 categories at around .075 to .1, and 600-700 following thereafter with growing estimated returns. This could be because those with higher credit scores pay their loans off quicker, at lower rates.
Interestingly, there are a bevy of loans at the 600-700 credit score level that do not pay off loans that are less than 10,000 in total value. Even though they have credit scores similarly to those borrowing at higher dollar amounts, they were unable to pay their comparable smaller debts.
**Loan Original Amount, # of Investors, Credit Score
ggplot(data = subset(loans,!is.na(loans$csBucket)), aes(x = Investors, y = LoanOriginalAmount))+
geom_point(alpha = 1/3, aes(color = csBucket))+
geom_vline(xintercept = median(loans$Investors))+
ggtitle('Loan Original Amount by Number of Investors and Credit Score Bucket')
The graph above shows that the total amount of investors increases as the loan original amount increases, and invariably, the higher credit score users are more adept at getting additional investors. In the scatterplot, you hardly see any 400-700 credit score borrowers beyond the overall median line.
Interestingly, the higher end credit score borrowers of 800-900 generally have a # of investors per loan that is higher than the median and higher than there lesser counterparts, even twhen the loan original amount is the same, this means more individuals are investing smaller amounts per individual loan.
Loan Original Amount, Loan Investors, Prosper Rating
We run the tables below to view which Prosper Rating has the most loans and the highest loan amounts, we find that a score of 7 receives the highest median loan and a score of 1-2 have the lowest medians. This may be an indication of the loan worthiness of the borrowers - thus, we assue 7 to be the best loan for chance of repayment and 1 being the worse.
table(loans$ProsperRating..numeric.)##
## 1 2 3 4 5 6 7
## 6935 9795 14274 18345 15581 14551 5372by(loans$LoanOriginalAmount, loans$ProsperRating..numeric., summary)## loans$ProsperRating..numeric.: 1
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 3000 4000 3463 4000 16800
## --------------------------------------------------------
## loans$ProsperRating..numeric.: 2
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 3600 4000 4586 5000 15900
## --------------------------------------------------------
## loans$ProsperRating..numeric.: 3
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 4000 6100 7083 10000 15000
## --------------------------------------------------------
## loans$ProsperRating..numeric.: 4
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 5000 10000 10392 15000 25000
## --------------------------------------------------------
## loans$ProsperRating..numeric.: 5
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 6000 10000 11622 15000 35000
## --------------------------------------------------------
## loans$ProsperRating..numeric.: 6
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 5850 10000 11460 15000 35000
## --------------------------------------------------------
## loans$ProsperRating..numeric.: 7
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 1000 6000 10940 11584 16000 35000ggplot(data = loans, aes(x = Investors, y = LoanOriginalAmount))+
geom_point(alpha = 1/20, position = 'jitter', aes(color = loans$ProsperRating..numeric.))+
geom_vline(xintercept = median(loans$Investors))+
ggtitle('Loan Original Amount by Number of Investors and Numeric Prosper Rating')
The graph above shows that, as the number of investors and the loan original amount increases, more high-quality loans of Prosper Ratings of 4-5-6-7 are prevalent.
Delinquencies 7 Years Loan Investors, Prosper Rating Numeric
ggplot(data = loans_by_employment, aes(x = DelinquenciesLast7Years, y = LoanOriginalAmount))+
geom_point(alpha = 1/2, position = 'jitter', aes(color = loans_by_employment$EmploymentStatus))+
geom_vline(xintercept = mean(loans_by_employment$DelinquenciesLast7Years), color = 'black')+
ggtitle('Loan Original Amount by Delinquencies Last 7 Years and Employment Status')## Warning: Removed 88 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_vline).
When looking at the loan original amount and delinquencies the last 7 years, it is no surprise that the majority of points on the graph are those that are employed, even when transparency is added for overplotting. With the “employed” category as “red”, you will notice the prevalence of red dots as the loan amount increases, and the lack of red dots as the delinquencies the last 7 years increase below $5,000 loan amounts.
This means that those who are not categorized as “employed” in the Prosper system have higher delinquencies in the past 7 years, and do not get the same level of loan as those who are employed.
Multivariate Analysis
Talk about some of the relationships you observed in this part of the
investigation. Were there features that strengthened each other in terms of
looking at your feature(s) of interest?
In this section, we wanted to look closer at what categories may be determining loan amounts, the amount of investors, and the delinquencies in the last 7 years. We noticed that those who were not categorized as “employed” saw themselves receiving loans of roughly less than 5,000. Those same individuals were likely to have a higher rate of delinquencies in the last 7 years than those categorized as “employed”, and their loan amounts were lesser than their employed counterparts even if the delinquencies in the last 7 years were the same.
We also discovered that Prospers numeric rating runs from 1-7, with 7 being the most trustworthy rating.
Were there any interesting or surprising interactions between features?
I was overall surprised to see that the number of investors increases as credit score and prosper rating increases. It was my inclination that if a loan were to be deemed safe or less risky, more investors would provide higher individual amounts towards that loan, thus, lowering the total amount of investors per loan.
OPTIONAL: Did you create any models with your dataset? Discuss the
strengths and limitations of your model.
We did not create any models with this dataset.
Final Plots and Summary
Tip: You’ve done a lot of exploration and have built up an understanding of the structure of and relationships between the variables in your dataset. Here, you will select three plots from all of your previous exploration to present here as a summary of some of your most interesting findings. Make sure that you have refined your selected plots for good titling, axis labels (with units), and good aesthetic choices (e.g. color, transparency). After each plot, make sure you justify why you chose each plot by describing what it shows.
Plot One
## Warning: Removed 88 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_vline).
Description One
The plot above shows the Loan Original Amount on the y-axis, the number of delinquencies in the last 7 years on the x-axis, with each plot indicating an employment status as a categorical variable.
This graph shows to me that, should you be employed, you have a marginal chance of receiving a loan from Prosper. Though the large majority of loans are at 0 delinquencies, it is important to notice that there are a great number of loans provided to people who have be delinquent dozens of times. You are more likely to receive a greater loan amount, however, if your employment status is “employed”
Plot Two
Description Two
The graph above shows the number of investors per loan on the x-axis, the total loan original amount on the y-axis, with the categorical variable of credit score bucket. This plot shows that, as the loan amount increases, the number of investors increases as well.
We already know from prior graphs that higher loan amounts are more likely to be people employed with no delinquencies on their account, couple that with higher credit scores and higher loan amounts are generally more safe. We see that, as loan amounts increase, the number of investors per loan also increases.
This, to me, is a strange phenomenmon, as I would have guessed that, if a loan were to be less risky, investors would invest greater amounts towards that loan, thus limiting the total amount of investors per loan.
The plot shows borrowers with credit scores between 700-900 are generally receiving more investors at higher loan amounts than other credit scores.
Plot Three
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Description Three
The above plot shows the estimated return per loan on the x-axis, with the loan original amount on the y-axis and the credit score bucket as the categorical variable.
This plot shows that estimated returns will generally fall between .05 and .15, are nearly normally distributed, and will be somewhat dependent on the credit score of the borrower. Borrowers with higher credit scores are shown to provide less returns to investors, likely due to lower interest rates and ability to pay back a loan quickly.
The plot also shows that estimated returns for higher credit score borrowers are largely the same regardless of the loan amount, showing that loan amount does not really affect return rate, and vice versa.
Reflection
Tip: Here’s the final step! Reflect on the exploration you performed and the insights you found. What were some of the struggles that you went through? What went well? What was surprising? Make sure you include an insight into future work that could be done with the dataset.
The Prosper data was quite large and there were a number of variables that were omitted from this analysis simply due to time and expectations from the course. With greater time, one could examine the areas such as investment from friends to see if certain credit score users or certain Prosper loans are more likely to get loans from their friends.
It was interesting to note that there are a higher number of investors per loan, particularly when the credit score of the borrower is high. This goes against my intution that single or a handful of investors would want to buy out a loan completely. This potentially may show some skepticism of the Prosper platform.
I did not conduct any analysis of loan variables over time, as my questions were more focused on what affects a loan amount and the amount of investors investing in said loan. It may be interesting to explore whether estimated returns lowered or expanded overtime for Prosper loans.